Tension control in actuation of jointed instruments

ABSTRACT

A medical instrument system includes actuators, a medical instrument, and a control system operably connected to the actuators. The medical instrument includes an end portion and transmission systems, each of which couples the end portion to an actuator of the actuators such that the actuators are operable to drive the transmission systems to move the end portion. The control system is configured to execute operations including determining a difference between a current configuration of the end portion and a desired configuration of the end portion, and operating the actuators to apply tensions to the transmission systems based on the difference and based on constant offset tensions. The constant offset tensions are independent of current tensions experienced by the transmission systems.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a U.S. National Stage Application under 35 USC § 371and claims the benefit of International Patent Application No.PCT/US2018/050151 filed on Sep. 10, 2018, which claims priority to U.S.Provisional Pat. Application No. 62/584,608, filed Nov. 10, 2017, thedisclosure of each of which is hereby incorporated by reference in itsentirety.

BACKGROUND

Robotic procedures often employ instruments that are controlled with theaid of a computer or through a computer interface. Such instruments mayinclude one or more articulable portions (e.g. joints) and be controlledthrough the use of tension-carrying elements.

SUMMARY

In one aspect, a medical instrument system includes actuators, a medicalinstrument, and a control system operably connected to the actuators.The medical instrument includes an end portion and transmission systems,each of which couples the end portion to an actuator of the actuatorssuch that the actuators are operable to drive the transmission systemsto move the end portion. The control system is configured to executeoperations including determining a difference between a currentconfiguration of the end portion and a desired configuration of the endportion, and operating the actuators to apply tensions to thetransmission systems based on the difference and based on constantoffset tensions. The constant offset tensions are independent of currenttensions experienced by the transmission systems.

In another aspect, a method of operating an instrument includesdetermining a difference between a current configuration and a desiredconfiguration of an end portion of the instrument, and operatingactuators to apply tensions to transmission systems. The transmissionsystems are coupled to move the end portion. The tensions are based onthe difference and constant offset tensions. The constant offsettensions are independent of current tensions experienced by thetransmission systems.

In another aspect, an instrument system includes actuators, aninstrument, and a control system operably connected to the actuators.The instrument includes an end portion and transmission systems, each ofwhich is couples the end portion to an actuator of the actuators suchthat the actuators are operable to drive the transmission systems tomove the end portion. The control system is configured to executeoperations including determining a difference between a currentconfiguration of the end portion and a desired configuration of the endportion, and determining tensions to apply to the transmission systemsbased on the difference. A tension of the tensions is maintained at amaximum tension and a remainder of the tensions is no more than themaximum tension.

In another aspect, one or more non-transitory computer readable mediastoring instructions that are executable by a processing device isfeatured. Upon execution of the instructions, the processing deviceperforms operations including determining a difference between a currentconfiguration of an end portion of an instrument and a desiredconfiguration of the end portion of the instrument, determining firsttensions to apply to transmission systems based on the difference, andoperating actuators to apply second tensions to the transmissionsystems. The second tensions are based on the first tensions andconstant offset tensions. The constant offset tensions are independentof current tensions experienced by the transmission systems.

Advantages of the foregoing can include those described below and hereinelsewhere.

In accordance with an aspect of the invention, control systems andmethods for an instrument having multiple degrees of freedom usedifferences between a current configuration/velocity of the instrumentand a desired configuration/velocity of the instrument to determine andcontrol the forces that proximal actuators apply to the instrumentthrough a set of transmission systems. The use of applied force andfeedback indicating the resulting configuration of a medical instrumentallows robotic control of the medical instrument, even if transmissionsystems of the instrument have non-negligible compliance between theproximal actuators and remote actuated elements. The feedback approachparticularly allows precise instrument operation even when theconfiguration of the instrument cannot be directly inferred from thepositions of the proximal actuators.

In one embodiment of the invention, the configuration of an end effectoror tip is measured or otherwise determined, and the differences betweenthe current and desired configurations of the tip are employed indetermining the required joint torques and the applied forces needed toachieve the desired tip configuration. Embodiments of this controlmethod can allow selection of the dynamic behavior of the tip, forexample, to facilitate the instrument interaction with tissue, whilepermitting flexibility in other portions of the instrument.

In another embodiment of the invention, the configuration of each jointin an instrument is measured, and the differences between current anddesired joint configurations are used to determine the actuator forcesneeded to move all of the joints to desired configurations.

One specific embodiment of the invention is a medical system thatincludes multiple joints, actuators, and transmission systems. Thetransmission systems have proximal ends respectively coupled to theactuators, and each of the transmission systems has a distal endattached to an associated one of the joints to allow the transmission ofa force for articulation of the associated joint. A sensor in themedical system generates a measurement indicative of a configuration ofthe joints or the instrument tip, and a control system operates theactuators to apply forces to the transmission systems, receives theconfiguration measurements from the sensor, and uses the configurationmeasurements to determine the actuation forces applied to thetransmission systems.

Although some of the examples described herein often refer to medicalprocedures and medical instruments, the techniques disclosed also applyto non-medical procedures and non-medical instruments. For example, theinstruments, systems, and methods described herein may be used fornon-medical purposes including industrial uses, general robotic uses,manipulation of non-tissue work pieces, and/or cosmetic improvements.Other non-surgical applications include use on tissue removed from humanor animal anatomies (without return to a human or animal anatomy) or onhuman or animal cadavers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates features of a robotically controlled medicalinstrument.

FIG. 2 illustrates a medical instrument that can be operated using acontrol process in accordance with an embodiment of the invention thatcontrols the force applied through a compliant transmission system tocontrol an articulated vertebra of the instrument.

FIG. 3A illustrates a medical instrument in which a control process inaccordance with an embodiment of the invention can operate with atransmission system having minimum and maximum force transfer to operatea mechanical joint.

FIG. 3B shows an embodiment of the invention in which a joint includes acontinuously flexible structure.

FIG. 3C illustrates positions of a pair of tendons used to control asingle degree of freedom of motion in the joint of FIG. 3B.

FIG. 4 schematically illustrates a robotic medical system andparticularly shows quantities used in an embodiment of the inventionthat controls a remote joint connected to actuators through complianttransmission systems.

FIG. 5A is a flow diagram of a control process in accordance with anembodiment of the invention.

FIG. 5B is a flow diagram of a process for determining a tensioncorrection associated with a difference between an actuator velocity anda joint velocity.

FIG. 5C is a flow diagram of a process for determining a tensioncorrection associated with a difference between the velocities ofactuators manipulating the same joint.

FIG. 5D illustrates a function for control of a maximum and minimumapplied tension.

FIG. 6 schematically illustrates a robotic medical system andparticularly shows quantities used in an embodiment of the inventionthat controls a multi jointed instrument.

FIG. 7A is a flow diagram of a process in accordance with an embodimentof the invention that selects applied tensions based on differencesbetween measured and desired joint configurations.

FIG. 7B is a flow diagram of a process in accordance with an embodimentof the invention that selects applied tensions based on differencesbetween measured and desired tip configurations.

FIG. 8A is a side view of a portion of a multi jointed instrument thatcan be operated using drive force control in accordance of an embodimentof the invention to control joints with parallel actuation axes.

FIGS. 8B and 8C respectively show side and end views of a portion of amulti jointed instrument having joints with perpendicular actuation axesthat can be operated using drive force control in accordance with anembodiment of the invention.

FIG. 9A shows an embodiment of the invention in which a joint includes acontinuously flexible structure that provides two degrees of freedom ofmotion.

FIGS. 9B and 9C illustrate embodiments of the invention respectivelyemploying four and three tendons to control two degrees of freedom ofmotion in the joint of FIG. 9A.

FIG. 9D shows an embodiment of a two jointed medical instrument in whicheach joint includes a continuously flexible structure and provides twodegrees of freedom of motion.

FIG. 9E illustrates an embodiment of the invention employing six tendonsto control four degrees of freedom of motion provided by the two jointsin the instrument of FIG. 9D.

FIG. 10 schematically illustrates a robotic medical system andparticularly shows quantities used in another embodiment of theinvention that controls a multi jointed instrument.

FIG. 11 is a flow diagram illustrating a process in accordance with anembodiment of the invention that determines tensions through sequentialevaluation of joints in a multi jointed instrument.

FIG. 12A is a simplified diagram of a medical instrument systemaccording to some embodiments.

FIG. 12B is a simplified diagram of a medical instrument with anextended medical tool according to some embodiments.

DETAILED DESCRIPTION

In accordance with an aspect of the invention, a medical instrument canbe controlled via transmission systems driven by actuators to repositionjoints of the medical instrument and thereby move an end portion of themedical instrument. A human system operator (e.g., a surgeon) canindicate a currently desired configuration and/or a currently desiredvelocity for the medical instrument, while an actualconfiguration/velocity of the instrument can be determined or estimated,e.g., through measurements by a sensor. In some cases, the actualconfiguration and/or the actual velocity can be measured using a sensorthat generates measurements indicative of the actual configurationand/or the actual velocity. Forces, tensions, or torques can then beselected according to the desired and measured configurations andapplied through the transmission systems to move the instrument towardits desired configuration. The selection criteria for the applied force,tension, or torque can be altered if prior selections of the appliedforce, tension, or torque resulted in the joint overshooting or failingto reach a desired position.

FIG. 1 , for example, shows a robotically controlled instrument 100having a structure that is simplified to illustrate basic workingprinciples of some robotically operated instruments. (As used herein,the terms “robot” or “robotically” and the like include aspects thatinvolve teleoperation or are not teleoperated.) Instrument 100 includesa tool or end effector 110 at the distal end of an elongated shaft ormain tube 120. In the illustrated example, end effector 110 is a jawedtool such as forceps or scissors having separate jaws 112 and 114, andat least jaw 112 is movable to open or close relative to jaw 114. In useduring a medical procedure, end effector 110 on the distal end of maintube 120 may be inserted through a small incision in a patient andpositioned at a work site within the patient. Jaws 112 may then beopened and closed, for example, during performance of surgical tasks,and accordingly must be precisely controlled to perform only the desiredmovements. Some implementations of instrument 100 has many degrees offreedom of movement in addition to opening and closing of jaws 112 and114 to aid in performing procedures.

The proximal end of main tube 120 attaches to a transmission or drivemechanism 130 that is sometimes referred to as backend mechanism 130.Tendons 122 and 124 run from backend mechanism 130 through main tube 120and attach to end effector 110. A tendon such as tendons 122, 124 mayinclude stranded cables, rods, metal bands, tubes, or combinations ofsuch structures,

Some instruments, including medical instruments such as surgicalinstruments, include additional tendons (not shown in FIG. 1 ) thatconnect backend mechanism 130 to other actuated members of end effector110, a wrist mechanism (not shown), or actuated vertebrae in main tube120; such architecture backend mechanism 130 can manipulate the tendonsto operate end effector 110 and/or other actuated elements of instrument100.

FIG. 1 illustrates jaw 112 as having a pin joint structure 116 thatprovides a single degree of freedom for movement of jaw 112. Two tendons122 and 124 are attached to jaw 112 and to a pulley 132 in backendmechanism 130, so that rotations of pulley 132 cause jaw 112 to rotate.

Pulley 132 is attached to a drive motor 140, which may be at the end ofa mechanical arm (not shown), and a control system 150 electricallycontrols drive motor 140. In some implementations, the instrument 100includes part or all of control system 150. In some implementations thecontrol system 150 is partially or entirely separate from the instrument100. In some implementations, control system 150 includes a computingsystem along with suitable software, firmware, and peripheral hardware.Among other functions, in some implementations control system 150provides a user (e.g. a system operator, medical personnel or surgeon ifa medical system) with an image of the work site and end effector 110and provides a control device or manipulator that the surgeon canoperate to control the movement of end effector 110. The image of thework site may be provided monoscopically, stereoscopically, etc.

The software or firmware needed for interpretation of user manipulationsof the control device and for generation of the motor signals that causethe corresponding movement of jaw 112 c can be complex, and aregenerally complex in a real robotic medical instrument. To consider onepart of the control task, the generation of the control signals fordrive motor 140 commonly employs the relationship between the angle orposition of jaw 112 and the angle or position of drive motor 140 orpulley 132 in backend mechanism 130. If the tendons 122 and 124 arerigid (e.g., if stretching of tendons is negligible), control system 150can use a direct relationship between the angular position of drivemotor 140 and the angular position of jaw 112 as defined by the geometryof instrument 100 in determining the control signals needed to move jaw112 as a surgeon directs. Minor stretching of tendons 122 and 124, forexample, under a working load, can be handled by some mathematicalmodels relating motor position to effector position. However, if themechanical structure including end effector 110, tendons 122 and 124,and backend mechanism 130 has a high degree of compliance, arelationship between the angular position of motor 140 (or pulley 132)and the angular position of jaw 112 may be difficult to model withsufficient accuracy for a medical instrument.

It should be noted that in the following, the joint of the medicalinstrument can be a pin joint structure or a structure that provides oneor more degrees of freedom of motion to the instrument tip. Forinstance, a joint can be a continuously flexible section or acombination of pin joints that approximates a continuously flexiblesection or a single rotary joint that is not purely revolute butprovides also some rolling joint. See, for example, U.S. Pat. No.7,320,700, by Cooper et Al., entitled “Flexible Wrist for SurgicalTool,” and U.S. Pat. 6,817,974, by Cooper et Al., entitled “SurgicalTool Having a Positively Positionable Tendon-Actuated Multi-disk WristJoint.”

It should also be noted that the actuator positions can be servocontrolled to produce the desired instrument tip motion or position.Such an approach may be effective as long as the transmission systemsbetween the actuators and the instrument joints are rigid for allpractical purposes. See, for example, U.S. Patent 6,424,885, entitled“Camera Referenced Control in a Minimally Invasive Surgical Apparatus.”Such an approach can also be effective if the flexibility of thetransmission system can be modeled exactly and a model included in thecontroller as described in U.S. Pat. App. Pub. No. 2009/0012533 Al,entitled “Robotic Instrument Control System” by Barbagli et Al.

Although some of the examples described herein often refer to medicalprocedures and medical instruments, the techniques disclosed also applyto non-medical procedures and non-medical instruments. For example, theinstruments, systems, and methods described herein may be used fornon-medical purposes including industrial uses, general robotic uses,manipulation of non-tissue work pieces, and/or cosmetic improvements.Other non-surgical applications include use on tissue removed from humanor animal anatomies (without return to a human or animal anatomy) or onhuman or animal cadavers.

FIG. 2 illustrates a portion of an instrument 200 that may beimplemented as a compliant medical instrument. Instrument 200 has atransmission system. In addition to examples of transmission systemsdescribed herein, examples of transmission systems are further describedin U.S. Pat. Application Ser. No. 12/494,797, entitled “CompliantSurgical Device,” which is hereby incorporated by reference in itsentirety. Instrument 200 includes a jointed element 210 that ismanipulated through control of the respective tensions in tendons 222and 224. In general, instrument 200 may contain many mechanical jointssimilar to jointed element 210, and each joint may be controlled usingtendons similar to tendons 222 and 224. In an exemplary embodiment,instrument 200 is an entry guide that can be manipulated to follow anatural lumen within a patient. An entry guide would typically include aflexible outer sheath (not shown) that surrounds vertebrae (includingelement 210) and provide one or more central lumens through which othermedical instruments can be inserted for access to a work site.Compliance is particularly desirable in entry guides to prevent anaction or reaction of the entry guide from harming surrounding tissuethat may move or press against the entry guide. However, other types ofmedical instruments may also benefit from compliant drive mechanisms ofthe type illustrated in FIG. 2 .

Instrument 200 includes a backend mechanism 230 that includes one ormore transmission systems connecting an end portion, e.g., jointedelement 210, to one or more actuators. For example, tendons 222 and 224provides a compliant transmission system connecting to jointed element210 to drive motors 242 and 244. In particular, backend mechanism 230includes spring systems 235 attached to tendons 222 and 224 and drivemotors 242 and 244. Each spring system 235 in FIG. 2 includes amechanical drive system 232 and a constant force spring 234. Each drivesystem 232 couples a motor 242 or 244 and converts rotational motion ofthe drive motor 242 or 244 into linear motion that changes the constantforce applied by the associated constant force spring 234 to tendon 222or 224. In the illustrated embodiment, each constant force spring 234includes a conventional Hooke’s law spring 236 and a cam 238. Eachspring 236 connects to an associated drive system 232 so that the linearmotion of drive system 232 moves a proximal end of the spring 236. Eachcam 238 has a first guide surface on which a cable 237 attached to thedistal end of the associated spring 236 attaches and rides and a secondguide surface on which a portion of tendon 222 or 224 attaches andrides. The guide surfaces of each cam 238 generally provide differentmoment arms for the action of the attached cable 237 and the attachedtendon 222 or 224 and are shaped so that the tension in tendon 222 or224 remains constant as the paying out or hauling in of a length oftendon 220 or 224 changes the force applied by the attached spring 236.Each surface of each cam 238 may be a spiral surface that extends forone or more revolutions in order to provide the desired range ofmovement of the tendon 222 and 224 while maintaining a constant tensionin tendon 222 or 224.

Each drive system 232 controls the position of the proximal end of thecorresponding spring 236 and thereby influences the amount of baselinestretch in the corresponding spring 236 and the tension in the attachedtendon 222 or 224. In operation, if a drive system 232 in a springsystem 235 pulls on the attached spring 236, the spring 236 begins tostretch, and if the element 210 and tendon 222 or 224 attached to thespring system 235 are held fixed, the force that spring 236 applies tocam 238 increases and therefore the tension in the attached tendon 222or 224 increases. The tendon 222 and 224 each may include a cable or aportion of a cable. Accordingly, the tensions in tendons 222 and 224depend linearly (in accordance with Hooke’s law, the moment arms of cam238, and the spring constant of spring 236) on movement of the proximalends of respective springs 236, but each spring system 235 behavesasymmetrically. For example, each spring system 235 acts with constantforce in response to external or distal forces that move tendon 222 or224. Constant force spring 234 and drive system 232 can be alternativelyimplemented in a variety of ways such as those described further inabove-referenced U.S. Pat. Application Ser. No. 12/494,797.

Jointed element 210 has a single degree of freedom of motion (e.g.,rotation about an axis) and generally moves when drive motor 242 or 244rotates a drive system 232 to change the force applied by the attachedconstant force spring 234. Control system 250 can use a sensor 260 tomeasure the orientation of element 210. A control process as describedfurther below uses such measurements for calculation of applied forcesneeded to manipulate jointed element 210 or applied torques drive motor242 or 244 to manipulate jointed element 210.

In some cases, the drive mechanism can be compliant so that externalforces can move element 210 without a corresponding rotation of drivesystem 232. As a result, the relationship between the position ororientation of jointed element 210 and the position of drive system 232or drive motor 242 may not be fixed. Sensor 260 may be, for example, ashape sensor, which can sense the shape of jointed element 210 along alength of instrument 200 including element 210. Some examples of shapesensors are described in U.S. Pat. App. Pub. No. US 2007/0156019 A1(filed Jul. 20, 2006), entitled “Robotic Surgery System IncludingPosition Sensors Using Fiber Bragg Gratings” by Larkin et al., and U.S.Pat. Application Ser. 12/164,829 (filed Jun. 30, 2008) entitled “Fiberoptic shape sensor” by Giuseppe M. Prisco, the entireties of both ofwhich are incorporated herein by reference. In some implementations, anysensor capable of measuring an angular position of jointed element 210could alternatively be used. For example, in some cases, the sensor cancorrespond to a sensor associated with a drive mechanism of instrument200, e.g., drive system 232, drive motor 242, or drive motor 244. Thesensor can include an encoder, a tachometer, or other appropriate sensorto measure a position or velocity of the mechanism. Based on a kinematicrelationship between position and velocity of jointed element 210 andposition and velocity of the drive mechanism, the measured position orthe measured velocity can be used to determine the position and thevelocity of the jointed element 210.

Instrument 200 has “back driving” capability when backend mechanism 230is detached from a motor pack, spring systems 235 still keep tendons 222and 224 from slacking and allow the distal portion of instrument to bemanually arranged (or posed) without damaging backend mechanism 230 orcreating slack in tendon 222 or 224. This “back driving” capability isgenerally a desirable property of a surgical instrument, particularly aninstrument with a flexible main tube that may be bent or manipulatedduring instrument insertion while the instrument is not under activecontrol by control system 250. For example, instrument 200 can bemanually posed, and the tendons within the main shaft do not experienceundue tension or slack.

Another example of a compliant transmission system for a joint in amedical instrument is illustrated in FIG. 3A. FIG. 3A shows an exemplaryembodiment of a medical instrument 300 that uses an actuation processthat permits a drive motor to freewheel or a drive tendon to sliprelative to the drive motor during instrument operation as described inU.S. Pat. Application Ser. No. 12/286,644, entitled “Passive Preload andCapstan Drive for Surgical Instruments,” which is hereby incorporated byreference in its entirety. An end portion of medical instrument 300 canbe manipulated. For example, the end portion can correspond to one of anend effector, a tip, or other device that can be controlled by theactuation process of medical instrument 300. In the example shown inFIG. 3A, medical instrument 300 has an end effector 310 at the end of amain tube 320, and a backend mechanism 330 manipulates tendons 322 and324, which run through main tube 320, to control a degree of freedom ofmotion of end effector 310. In the illustrated embodiment, tendons 322and 324 attach to a mechanical member in end effector 310 such thattensions in tendons 322 and 324 tend to cause end effector 310 to rotatein opposite directions about a pivot joint structure.

The joint structure of an end portion of instrument 300 in FIG. 3A isonly an example, and other joint mechanisms for end portions ofinstruments that provide a single degree of freedom of motion inresponse to tensions applied to a pair of tendons could be employed inalternative embodiments of the invention. FIG. 3B, for example,illustrates an embodiment in which the end effector 310 includes a jointsuch as commonly found in catheters, endoscopes for the gastrointestinaltract, the colon, and the bronchia; guide wires; or other endoscopicinstruments such as graspers and needles used for tissue sampling.

Main tube 320 can include a catheter that is able to flex or bend inresponse to forces applied through tendons 322 and 324. The catheterjoint may simply include an extrusion of a plastic material that bendsin response to a differential in the tension in tendons 322 and 324. Inone configuration, tendons 322 and 324 extend through lumens within thecatheter and attach to the end of the catheter as shown in FIG. 3C.Accordingly, the forces in tendons 322 and 324 can be used to bend thecatheter in the direction corresponding to the tendon 322 or 324 havinggreater tension. Bending of the catheter may be used, for example, tosteer the catheter during insertion. In some examples, distal sensor 360can measure the bend angle of the distal portion of the catheter tomeasure or compute the “joint” angle and velocity. In one particularembodiment, the bend angle can be defined as a tip orientation of thecatheter with respect to the base of the distal flexible portion of thecatheter. The backend and control architecture for the catheter joint ofend effector 310 of FIG. 3B can be identical to that of the embodimentof FIG. 3A, except that the measured joint angle and velocity can beconverted to tendon position and velocity by multiplication of thedistance between the actuator cable lumen and the center of the distalflexible portion.

Backend mechanism 330, which attaches to the proximal end of main tube320, acts as a transmission that converts torques applied by drivemotors 342 and 344 into tensions in respective tendons 322 and 324 andforces or torques applied to an actuated joint in end effector 310. Inthe illustrated embodiment, drive motors 342 and 344 can be direct driveelectrical motors that directly couple to capstan 332 and 334 aroundwhich respective tendons 322 and 324 wrap. In particular, tendon 322wraps for a set wrapping angle (that could be less than a full turn oras large as one or more turns) around the corresponding capstan 332 andhas an end that is not affixed to capstan 332 but extends from thecapstan 332 to a passive preload system 333. Similarly, tendon 324 wrapsfor a set wrapping angle around the corresponding capstan 334 and has anend extending from the capstan 334 to a passive preload system 335.Since tendons 322 and 324 are not required to be permanently attached tocapstans 332 and 334, tendon 322 and 324 may be able to slip relative tocapstans 332 and 334 and relative to the shaft of drive motors 342 and344 that respectively couple to capstans 332 and 334.

The proximal end of tendons 322 and 324 attach to respective passivepreload systems 333 and 335, each of which is implemented in FIG. 3A asa cam and a spring that together act as a constant force spring. Thespring can be one that generally can be modeled with Hooke’s law.Passive preload systems 333 and 335 are biased, so that capstans 332 and334 apply non-zero forces or tensions to tendons 322 and 324 throughoutthe range of motion of instrument 300. With this configuration, whencapstans 332 and 334 are free to rotate, passive preload systems 333 and335 control the tensions in tendons 322 and 324 and avoid slack intendons 322 and 324 by pulling in or letting out the required lengths oftendons 322 and 324. When backend mechanism 330 is detached from motors342 and 344, passive preload systems 333 and 335 still keep tendons 322and 324 from slacking and allow end effector 310 and main tube 320 (whenflexible) to be manually arranged (or posed) without damaging backendmechanism 330 or creating slack in tendon 322 or 324. Accordingly,instrument 300 also has “back driving” capability similar to thatdescribed above for instrument 200 of FIG. 2 .

End effector 310 can be operated using drive motors 342 and 344 underthe active control of control system 350 and human input (e.g., mastercontrol input in a master-slave servo control system). For example, whenmotor 342 pulls on tendon 322, the motor torque is transferred as anapplied tension in the distal portion of tendon 322. (A maximum tensionthat capstan 332 can apply to proximal portion of tendon 322 depends ona tension at which tendon 322 begins to slip relative to captain 332,but in general, the maximum tension actually used can be selected toprevent tendons 322 and 324 from slipping on capstans 332 and 334.) Atthe same time, when turning off the power to motor 344, allowing motor344 and capstan 334 to freewheel, tendon 324 can be kept at its minimumtension that is the constant force that passive preload system 335applies to proximal end of tendon 324 through the capstan 334. Thelarger tension in tendon 322 then tends to cause end effector 310 torotate counterclockwise in FIG. 3A. Similarly, turning off power tomotor 342 and powering motor 344 to apply force through tendon 324 toend effector 310 tends to cause end effector 310 to rotate clockwise inFIG. 3A. The ability of motor 342 and 344 to freewheel while tendons 322and 324 are under tension and the acceptance of slippage of tendons 322and 324 on capstans 332 and 334 do not permit control system 350 to relyon a fixed relationship between the angular positions of motor 340 andend effector 310. However, control system 350 can use a sensor 360 tomeasure the angular position of end effector 310 relative to the jointactuated through tendons 322 and 324.

The instruments of FIGS. 2, 3A, and 3B may have transmission systemsbetween actuators and actuated joints provide compliance that isdesirable, particularly for instruments with a flexible main tube.Transmission systems with compliance may also occur in more traditionalinstruments. For example, the known instrument of FIG. 1 may usesheathed or Bowden cables in sections of the instrument that bend androd elements in straight sections. The rod elements can reducestretching that interferes with the direct relationship of actuator andjoint positions. It may be desirable in some applications to use tendonsof more flexible material (e.g., polymer tendons where electricalinsulation or minimal friction is desired). Such tendons may introducean unacceptable amount of stretch for control processes relying on adirect relationship between actuator and joint position. Solid steelpull wires can also be used in or as transmission systems.

In accordance with one aspect of the current invention, controlprocesses for the medical instruments of FIGS. 2, 3A, and 3B orinstruments that otherwise have compliant transmission systems canemploy remote measurements of the position of a mechanical joint todetermine a tension to be applied to drive the mechanical joint. Inanother aspect, processes for the medical instruments of FIGS. 2, 3A,and 3B or instruments that otherwise have compliant transmission systemscan employ measurements of the position of actuators of the instrumentsto determine a tension to be applied to drive the mechanical joint. Thecontrol processes could also be employed for instruments having rigidtransmission systems. The control processes could also be employed forinstruments having rigid transmission systems. FIG. 4 schematicallyshows a generalization of a medical instrument 400 having a mechanicaljoint 410 having a degree of freedom of motion corresponding to an angleor position θ. The term position is used broadly herein to include theCartesian position, angular position, or other indication of theconfiguration of a degree of freedom of a mechanical system.

Joint 410 is connected through a transmission system 420 to an actuator440, so that joint 410 is remote from actuator 440, e.g., joint 410 maybe at a distal end of instrument 400 while actuator 440 is at theproximal end of instrument 400. In this regard, joint 410 forms part ofan end portion of instrument 400. In the illustrated embodiment,transmission system 420 connects joint 410 so that a tension T appliedby actuator 440 to transmission system 420 tends to rotate joint 410 ina clockwise direction. In general, transmission system 420 includes theentire mechanism used to transfer force from actuator 440 to joint 410,and actuator 440 may apply a force or torque to transmission system 420which results in a tension in a cable or other component of transmissionsystem 420. Such a tension can be generally proportional to the appliedforce or torque, so the term tension is intended to be used here withoutloss of generality to also indicate force or torque.

The transmission system 420 may be (but is not required to be) socompliant that a direct relationship between the position of joint 410and the position of actuator 440 would not be accurate enough forcontrol of joint 410. In this regard, in some examples, transmissionsystem 420 may be compliant, but a direct relationship is sufficientlyaccurate for use in control of joint 410. In some cases, transmissionsystem 420 may stretch, so that between a minimum and a maximum oftension T applied to transmission system 420, the difference in theeffective length of transmission system 420 may correspond to 45° ofjoint articulation. In contrast, a typical medical device allows forstretching that corresponds to no more than a few degrees of jointarticulation in order to be able to accurately model the position of thejoint based on actuator position. It should be understood that in thegeneral case compliance is not limited to a simple Hooke’s lawstretching of a spring structure. Transmission system 420 may include,for example, tendon 222 and at least a portion of backend mechanism 230in the embodiment of FIG. 2 or tendon 322 and at least a portion ofbackend mechanism 330 in the embodiment of FIG. 3A. In general, theresponse of transmission system 420 to a tension T applied at a proximalend of transmission system 420 and to external forces applied to joint410 or along the length of transmission system 420 may be difficult tomodel.

A sensor (not shown) measures position θ at remote joint 410 andprovides measured position θ to a control system 450. The sensor mayadditionally measure a velocity {dot over (θ)} for the movement of joint410, or velocity {dot over (θ)} may be determined from two or moremeasurements of position θ and the time between the measurements. Thesensor can include a distal sensor in which measured position θ isprovided to control system 450 through a signal wire (not shown)extending from the sensor at the distal end of instrument 400, throughthe main tube (not shown) of instrument 400 to control system 450 at theproximal end of the instrument. The signal wire can be an electricalwire, an optical fiber, or other signal wire capable of transmitting asignal.

Alternatively or additionally, the position of actuator 440 may besufficiently accurate for controlling joint 410. The sensor can includea sensor associated with actuator 440, e.g., an encoder, a tachometer,or other sensor to measure a position or a velocity of actuator 440.

Actuator 440, which can include drive motor 242 or 342 of FIGS. 2 or 3A,applies tension T to the proximal end of transmission system 420 andthrough transmission system 420 applies force or torque to joint 410. Insome cases, other forces and torques can also be applied to joint 410.For example, one or more other transmission systems 420 may be connectedto joint 410 and collectively apply a net tension or force that tends tocause joint 410 to rotate. In the illustrated embodiment of FIG. 4 , atransmission system 422 is connected to joint 410 and to an actuator442, so that tension in transmission system 422 tends to oppose appliedtension T and rotate joint 410 counterclockwise in FIG. 4 . Theadditional transmission system 422 or transmission systems connected tojoint 410 may be the same as transmission system 420, other than adifference in where transmission system 422 or transmission systemsconnect to joint 410.

Control system 450 can be a general purpose computer executing a programor a circuit wired to generate a drive signal that controls a tension Tthat actuator 440 applies to transmission system 420. When actuator 440is an electrical motor, the drive signal may be a drive voltage orcurrent that controls the torque output from actuator 440, and tension Tis equal to the motor torque divided by the effective moment arm atwhich tension T is applied to transmission system 420. As describedfurther below, control system 450 can calculate the magnitude of tensionT or the motor torque using a desired position θ.sub.D, a desiredvelocity {dot over (θ)}.sub.D for joint 410. This calculation can befurther based on one or more measurements of position θ for joint 410 atthe current and prior times or one or more measurements of positionθ.sub.A of actuator 440. In this regard the position θ for joint 410 cancorrespond to a position that is determined based on direct measurementsof the position θ for joint 410 or based on the one or more measurementsof position θ.sub.A of actuator 440. A user (e.g., a surgeon controllinga system including an instrument such as instrument 400) can providedesired position θ.sub.D and velocity {dot over (θ)}.sub.D bymanipulating a controller 460. The exact configuration of controller 460is not critical to the present invention except that controller 460 isable to provide signals from which values for the desired positionθ.sub.D and velocity {dot over (θ)}.sub.D can be determined. Manualcontrollers suitable for complex medical instruments generally providesignals that indicate many simultaneous instructions for movements ofthe medical instrument, and such movements may involve multiple jointsin the instrument. Suitable manipulators for use as controller 460 areprovided, for example, in the master controller of the da Vinci SurgicalSystem available from Intuitive Surgical, Inc.

The tension T needed to move joint 410 from its current position θ todesired position {dot over (θ)}.sub.D in a time interval Δt willgenerally depend on many factors including the effective inertia ofjoint 410 that resists applied tension T; the inertia of actuator 440which applies tension T, any other transmission systems 422 coupled tojoint 410 and applying a net effective force; external forces applied tojoint 410; internal and external frictional forces that oppose actuationof joint 410 or movement of transmission system; the current velocity{dot over (θ)} of joint 410; and internal and external damping forces.Many of these factors may vary depending on the working environment ofinstrument 400 and may be difficult to measure or model. However, modelscan be developed based on system mechanics or empirically for aparticular joint in a medical instrument. In one specific embodiment,control system 450 determines the tension T from the distal joint errors(θ.sub.D-θ) and ({dot over (θ)}.sub.D-{dot over (θ)}), which arerespectively the difference between the determined and desired positionsof joint 410 and the difference between determined and desiredvelocities of joint 410.

FIG. 5A is a flow diagram of a process 500 for controlling a medicalinstrument having the basic structure of instrument 400 of FIG. 4 .Process 500 begins in step 510 by determining a current value ofposition θ of joint 410 and determining a current value for the jointvelocity {dot over (θ)}. For example, the current value of position θ ofjoint 410 and the current value of the joint velocity {dot over (θ)} canbe determined from measurements taken by a sensor. Velocity {dot over(θ)} can be directly measured or determined or approximated using thecurrent position θ, a prior position θ′, a time interval Δt betweenmeasurements, for example, under the assumption of constant velocity(e.g., {dot over (θ)}=(θ-{dot over (θ)}ʹ)/Δt) or under the assumption ofconstant acceleration given a prior determination of velocity. Forexample, in some implementations, rather than directly measuring thecurrent value of position θ for joint 410, the current value ofposition0 is determined based on measurements of position θ.sub.A ofactuator 440. In this regard at step 510, measurements of positionθ.sub.A of actuator 440 are taken every time interval Δt, and thecurrent value of position θ is then determined based on the measuredposition θ.sub.A of actuator 440. Similarly, a current value of velocity{dot over (θ)} can be determined using measurements of position θ.sub.Aof actuator 440. Alternatively, the current value of velocity {dot over(θ)} can be determined using measurements of a velocity {dot over(θ)}.sub.A of actuator 440.

Following step 510, step 515 then acquires a desired position {dot over(θ)}.sub.D and a desired velocity {dot over (θ)}.sub.D for joint 410,and step 520 computes a difference or error (θ.sub.D-θ) between themeasured and desired positions and a difference or error ({dot over(θ)}-{dot over (θ)}) between the measured and desired velocities.

The position error computed in step 520 can be indicative of adifference between a current configuration of an end portion, e.g.,joint 410, and a desired configuration of the end portion, e.g., joint410. The position error and velocity error can be used to determinetension T required for joint 410 to reach the desired position 0.sub.D.Tensions described herein are not necessarily applied to transmissionsystems. Tensions described herein can refer to tensions that areapplied to transmission systems 420 or tensions that are determined ordetected and used for selecting another tension to apply to transmissionsystems 420. In the embodiment of FIG. 5A, applied tension T may includemultiple contributions, and the primary contribution is a distal tensionT.sub.DIST, which is determined as a function ƒ.sub.1 of position error(θ.sub.D-θ) and velocity error ({dot over (θ)}.sub.D-{dot over (θ)}).Distal tension T.sub.DIST can be independent of the position of theactuator, e.g., of the angle of the motor shaft, which allowsdetermination of distal tension T.sub.DIST even when there is no directrelationship between the position of joint 410 and the position ofactuator 440.

In one particular embodiment, the function f sub.1 is of the formEquation 1 below, where g1 and g2 are gain factors, C is a constant orgeometry dependent parameter, and T.sub.sign is a sign, i.e., ±1. SignT.sub.sign is associated with movement of joint 410 produced by tensionin transmission system 420 and may, for example, be positive (e.g., +1)if tension Tin transmission system 420 tends to increase the positioncoordinate θ and negative (e.g., -1) if tension T in transmission system420 tends to decrease the position coordinate θ. In another embodiment,function ƒ.sub. 1 imposes a lower bound on the force, for instance, inorder for the force to be always positive and sufficient to avoid slackin the transmission system. The parameter C can be a constant selectedaccording to known or modeled forces applied to joint 410 by otherportions of the system. For example, parameter C may be a constantselected to balance the torque caused by other transmission systemsapplying force to joint 410 or may account for expected friction orexternal forces. However, parameter C is not required to strictly be aconstant but could include non-constant terms that compensate forproperties such as gravity or mechanism stiffness that can beeffectively modeled, and accordingly, parameter C may depend on thedetermined joint position or velocity. The gain factors g1 and g2 can beselected according to the desired stiffness and dampening of joint 410.In particular, when joint 410 is used as a static grip, the net grippingforce or torque applied to tissue depends on the term g1(θ.sub.D-θ) ofEquation 1. For example, in some implementations, the force or torquethat the gripper achieves depends on this term g1(θ.sub.D-θ) and thecommanded position. Some implementations further impose limits on themaximum torque or force that can be achieved. In general, gain factorsg1 and g2 and constant C can be selected according to the desiredstiffness and dampening or responsiveness of joint 410 or according toan accumulation of error. For example, when inserting the instrument 400to follow a natural lumen within a patient, the gain factor g1 can beset to a low value to make joint 410 behave gently and prevent joint 410from harming surrounding tissue. After the insertion, the gain factor g1can be set to a higher value that allows the surgeon to perform precisesurgical task with the instrument.

ƒ.sub.1=T.sub.sign*(g1(θ.sub.D − θ) + g2({dot over(θ)}.sub.D − {dot over(θ)}) + C)

The term g1(θ.sub.D-θ)+g2({dot over (θ)}.sub.D-{dot over (θ)})+C ofEquation 1 can be used to approximately determine the torque, tension,or force currently required at joint 410 to rotate joint 410 to reachthe desired position θ.sub.D using transmission system 420 in a giventime Δt. In some implementations, the applied torque, tension, or forcedoes not move joint 410 to desired position θ.sub.D within given time Δtbut, rather, joint 410 asymptotically approaches desired positionθ.sub.D without reaching desired position θ.sub.D. The torque and forceor tension are related in that the torque is the product of the forceand an effective moment arm R, which is defined by the perpendiculardistance between the connection of transmission system 420 to joint 410and the rotation axis of joint 410. The effective moment arm R caneither be absorbed into gain factors g1 and g2 and constant C or used toconvert a calculated distal tension T.sub.DIST into a calculated torque.

Distal tension T.sub.DIST, with the proper choice of function fl, e.g.,proper selection of parameters g1, g2, and C in Equation 1, canapproximate the force that actuator 440 is required to apply to movejoint 410 in a manner that is responsive to manipulations by a humanoperator of manual controller 460. However, optional corrections areprovided by steps 530, 535, 540, and 550 under some conditions. Inparticular, optional steps 530 and 535 respectively compute a saturatedsum or integral I of the position error (θ.sub.D-θ) and calculate anintegral tension T.sub.INT. The integral tension T.sub.INT, which may bepositive, zero, or negative, can be added as a correction to distaltension T.sub.DIST, which was calculated in step 525. Integral tensionT.sub.INT is calculated as a function f.sub.2 of saturated integral Iand may simply be the product of integral I and a gain factor. Thesaturated integral I calculated in step 530 can simply be the sum forthe past N intervals of position errors (θ.sub.D-θ) or differences(θ.sub.D,i-θ.sub.i-1) between the measured position at the end of theinterval and the desired position that was to be achieved. The number Nof intervals involved in the sum may be limited or not, and integral Imay be saturated in that the magnitude of the integral is not permittedto exceed a maximum saturation value. The saturation value wouldgenerally be selected to cap the maximum or minimum value of integraltension T.sub.INT. However, the minimum and maximum values of integraltension T.sub.INT can alternatively be capped when calculating the valueof function f.sub.2.

Optional step 540 computes another correction referred to herein asproximal tension T.sub.PROX, which may be positive, zero, or negative.Proximal tension T.sub.PROX can be added to distal tension T.sub.DIST,which was calculated in step 525. FIG. 5B is a flow diagram of anexample process for implementing step 540 for computing proximal tensionT.sub.PROX. This example process for implementing step 540 begins instep 542 by reading a current value of a velocity {dot over (θ)}.sub. Aof actuator 440. Velocity {dot over (θ)}.sub.A can be measured by astandard tachometer, an encoder, or other appropriate sensor thatattaches at the base of actuator 440. To improve computationalefficiency, step 542 can also be scheduled to run between steps 510 and515 of FIG. 5A. Step 544 then computes the proximal velocity differenceor error e.sub.PROX, which is defined as the difference or error betweena desired velocity computed based on desired velocity {dot over(θ)}.sub.D of joint 410 and the current velocity computed based on thecurrent actuator velocity {dot over (θ)}.sub.A. In one particularembodiment, the desired velocity can be the product of the effectivemoment arm R, sign T. sub. sign, and desired velocity {dot over(θ)}.sub.D of joint 410, while the current velocity can be the productof an effective moment arm of the actuator 440 and actuator velocity{dot over (θ)}.sub.A. In the embodiment of FIG. 5B, proximal tensionT.sub.PROX is determined as a function f.sub.4 of proximal velocityerror e.sub.PROX. In one particular embodiment, the function f.sub.4 maysimply be the product of proximal velocity error e.sub.PROX and a gainfactor. The gain factor can be selected to provide an additionaldampening effect to transmission system 420.

Optional step 550 of FIG. 5A computes a pair tension T.sub.PAIR, whichmay be positive, zero, or negative correction to distal tensionT.sub.DIST, which was calculated in step 525. FIG. 5C is a flow diagramof an example process for implementing step 550 for computing the pairtension T.sub.PAIR. This example process 550 for implementing step 550begins in step 552 by reading a current value of velocity {dot over(θ)}.sub.A of actuator 440 and velocity values of all other actuatorsassociated with joint 410. In the system of FIG. 4 , there are twoactuators 440 and 442 coupled to joint 410 and two actuator velocities{dot over (θ)}.sub.A and {dot over (θ)}.sub.A′. Step 552 can bescheduled to run between steps 510 and 515 of FIG. 5A to improvecomputational efficiency. Step 556 then computes a pair velocitydifference or error ė.sub.PAIR, which can be defined as the differenceor error between the current velocities {dot over (θ)}.sub.A and {dotover (θ)}.sub.A′ of the actuators 440 and 442 associated to joint 410,when actuators 440 and 442 are substantially identical, e.g., have thesame effective moment arms for operation on respective transmissionsystems 420 and 422. In one particular embodiment, the current velocityerror e.sub.PAIR can be the product of the difference ({dot over(θ)}.sub.A-{dot over (θ)}.sub.Aʹ) and the effective moment arm ofactuators 440 and 442. In the embodiment of FIG. 6 , pair tensionT.sub.PAIR is determined as a function ƒ.sub.5 of pair velocity errore.sub.PAIR. In one particular embodiment, the function ƒ.sub.5 maysimply be the product of pair velocity error e. sub.PAIR and a gainfactor. The gain factor can be selected to provide additional dampeningeffect to transmission system 420.

Tension T is determined in step 560 of FIG. 5A as a function f.sub.3 ofsum of distal tension T.sub.DIST, proximal tension T.sub.PROX, pairtension T.sub.PAIR, and integral tension T.sub.INT. In some cases,constraints on maximum and minimum vales of tension T can be enforced.For example, in the embodiment of FIG. 5D, function f.sub.3 limits themaximum and minimum values of tension T. Maximum tension T.sub.MAX andminimum tension T.sub.MIN can be set in the programming of controlsystem 450 (e.g., in software). Actuators 440, 442 are operablyconnected to control system 450 and accordingly can be controlled bycontrol system 450 such that tension T does not exceed maximum tensionT.sub.MAX and such that tension T does not fall below minimum tensionT.sub.MIN. Maximum tension T.sub.MAX can be set to avoid damage to theinstrument resulting from large forces, and minimum tension T.sub.MINcan be set to inhibit slack in tendons in transmission systems 420 and422. This can ensure that tendons in transmission systems 420 and 422 donot become derailed or tangled. In some cases, only one of maximumtension T.sub.MAX and minimum tension T.sub.MIN is enforced by controlsystem 450, while in other cases, both are enforced.

Control system 450 can initiate enforcement of maximum tensionT.sub.MAX, minimum tension T.sub.MIN, or both maximum tension T.sub.MAXand minimum tension T.sub.MIN when instrument 400 is coupled toactuators 440, 442. In particular, maximum tension T.sub.MAX and minimumtension T.sub.MIN can be enforced upon actuators 440, 442 being coupledto transmission systems 420, 422. Instrument 400 can be configured suchthat tendons of transmission systems 420, 422 are slack absent anyexternal forces on transmission systems 420, 422. In this regard, whentendons of transmission systems 420, 422 are decoupled from actuators440, 442, the tendons can be slack. When transmission systems 420, 422are coupled to actuators 440, 442, tension in the transmission systems420, 422 below minimum tension T.sub.MIN can be detected, therebycausing control system 450 to enforce minimum tension T.sub.MIN andoperate actuators 440, 442 in manner that causes tension T to be equalto or greater than minimum tension T.sub.MIN. Tension T can be appliedto enforce minimum tension T.sub.MIN and achieve desired positionθ.sub.D and/or desired velocity {dot over (θ)}.sub.D.

Rather than being set in software, in some cases, a complianttransmission system may itself have a minimum or maximum tension withproper design in the backend mechanism. For example, a transmissionsystem illustrated in FIG. 3A has a minimum tension T.sub.MIN controlledby the setting of preload system 333 or 335 when motor/actuator 342 or344 is freewheeling and a maximum tension T.sub.MAX resulting fromslipping when the torque of the couple motor 342 or 344 exceeds thepoint when the tendon 322 or 324 slips on capstan 332 or 334. Ingeneral, it is

Step 565 of FIG. 5A generates a control signal that causes actuator 440to apply tension T calculated in step 560. For example, the controlsignal when actuator 440 is a direct drive electrical motor may be adrive current that is controlled to be proportional to calculatedtension T. Control system 450 in step 570 causes actuator 440 to applyand hold the calculated tension T for a time interval Δt, during whichtime, joint 410 moves toward the current desired position θ.sub.D. Whenchanging the tension T, the application of the full tension T will bedelayed by a time depending on the inertia of actuator 440. Preferably,the inertia of actuator 440 is relatively small for rapid response. Forexample, the inertia of a drive motor acting as actuator 440 wouldpreferably be less than five times the inertia of joint 410. After timeΔt, process 500 branches back to step 510 to repeat measurement of thejoint position, acquisition of the target position and velocity, andcalculation of the tension T to be applied during the next timeinterval. In general, time Δt should be small enough to provide motionthat appears to be smooth to the operator of the instrument and whichdoes not cause undesirable vibrations in the instrument. For example,calculating and setting tension T two hundred and fifty times per secondor more will provide movement that appears smooth to the human eye andwill provide instrument operation that is responsive to human commands,e.g., to human manipulation of controller 460. Use of the errors in thecalculation of the tension T will generally cause joint 410 to convergeon the desired positions with or without the computation of integraltension T.sub.INT and without detailed modeling or measurement of theinstrument or the external environment. However, as described above,parameters such as gains g1 and g2 used in calculating the appliedtension T can be tuned for specific instruments and further tuned in useto compensate for changes in the external environment of the instrument.

The tension that actuator 442 applies to transmission system 422 canalso be controlled using control process 500 of FIG. 5A, and parametersused in process 500 for actuator 442 and transmission system 422 can bethe same or different from those used for actuator 440 and transmissionsystem 420 based on the similarities and differences of actuator 442 andtransmission system 422 when compared to actuator 440 and transmissionsystem 420. In particular, the sign value T.sub.sign for actuator 442 inthe configuration of FIG. 4 will be opposite to the sign valueT.sub.sign for actuator 440 because transmission systems 422 and 420connect to rotate joint 410 in opposite directions. As a result, theprimary tension contribution T.sub.DIST calculated in step 525 willtypically be negative for one actuator 440 or 442. Step 560, whichcalculates the applied tension T, can set a negative tension sumT.sub.DIST+T.sub.PROX+T.sub.PAIR+T.sub.INT to the minimum tensionT.sub.MIN as shown in FIG. 5D. Accordingly, parameters, e.g., constantC, for the calculation of distal tension T.sub.DIST in step 525 cangenerally be selected based on the assumption that the other actuatorwill apply the minimum tension T.sub.MIN.

The principles described above for control of a single joint in amedical instrument can also be employed to simultaneously controlmultiple joints in an instrument. FIG. 6 schematically illustrates amulti jointed medical instrument 600 and some quantities used in controlprocesses for instrument 600. Instrument 600 includes L joints 610-1 to610-L, generically referred to herein as joints 610. Each joint 610provides a range of relative positions or orientations of adjacentmechanical members and typically has one or two degrees of freedom ofmotion as described further below. Joints 610 of instrument 600 providea total of N degrees of freedom, where the number N of degrees offreedom is greater than or equal to the number L of joints 610, and theconfigurations of degrees of freedom of joints 610 can be describedusing N-components or a vector θ. An N-component velocity vector {dotover (θ)} is associated with the vector θ. Torques to τ.sub.1 toτ.sub.N, which move joints 610-1 to 610-L, respectively correspond tothe N components of vector θ in that torques τ.sub.1 to τ.sub.N tend tocause respective components of vector θ to change.

Joints 610 are actuated using M transmission systems 620-1 to 620-M(generically referred to herein as transmission systems 620) and Mactuators 640-1 to 640-M (generically referred to herein as actuators640). Transmission systems 620 and actuators 640 can be similar oridentical to transmission systems 420 and actuators 440, which aredescribed above with reference to FIG. 4 . In general, the number M oftransmission systems 620 and actuators 640 is greater than the number Nof degrees of freedom, but the relationship between M and N depends onthe specific medical instrument and the mechanics of joints in theinstrument. For example, a joint 610 providing a single degree offreedom of motion may be actuated using two transmission systems 620,and a joint 610 providing two degrees of freedom may be actuated usingthree or four transmission systems 620. Other relationships betweendegrees of freedom and actuating transmission systems are possible.Control system 650 operates actuators 640-1 to 640-M to selectrespective tensions T.sub. 1 to T.sub.M that actuators 640-1 to 640-Mrespectively apply to transmission systems 620-1 to 620-M.

Control system 650 for instrument 600 can use one or more measurementsrepresentative of position and velocity vectors θ and {dot over (0)} todetermine position and velocity vectors θ and {dot over (θ)}, e.g., toestimate position and velocity vectors θand {dot over (0)}. In somecases, control system 650 for instrument 600 can use one or more sensorsto determine position and velocity vectors θand {dot over (0)} andassociated with joints 610. The one or more sensors can include a distalsensor (not shown) to determine position and velocity vectors θ and {dotover (0)} associated with joints 610. (Position and velocity are usedhere to include the values and movement of linear or angularcoordinates.) Alternatively control system 650 can use one or moreproximal sensors associated with actuators 640 to determine position andvelocity vectors θ and {dot over (θ)}. Each actuator 640 can include acorresponding proximal sensor to generate measurements indicative ofposition and velocity vectors θ and {dot over (0)}. Proximal sensors caninclude, for example, encoders, tachometers, and other appropriatesensors to be coupled with actuators 640. In some cases, proximalsensors are sensors of instrument 600. Alternatively, proximal sensorsare associated with actuators 640.

Control system 650 also determines a desired configuration of joints610. The desired configuration can be indicative of desired position andvelocity vectors θ.sub.D and {dot over (θ)}.sub.D of joints 610. Asdescribed further below, the desired position and velocity vectorsθ.sub.D and {dot over (θ)}.sub.D depend on input from a manualcontroller 660 that may be manipulated by a surgeon using instrument600. In general, the desired position and velocity vectors θ.sub.D and{dot over (θ)}.sub.D will further depend on the criteria or constraints,e.g., a set of values indicative of minimum tensions in transmissionsystems 620, a set of values indicative of maximum tensions intransmission systems 620, etc., defined in the control processimplemented using control system 650.

FIG. 7 illustrates a control process 700 in accordance with anembodiment of the invention for controlling a multi jointed instrumentsuch as instrument 600 of FIG. 6 . Process 700 begins in step 710 bydetermining joint position vector θ from one or more sensors, e.g.,associated with the instrument or coupled with actuators 640. Thevelocity vector {dot over (θ)} can also be determined, for example,using a direct measurement of joint movement or through calculation ofthe change in position measurements between two times.

In some examples, positions of actuators 640 can be considered to bemechanically coupled to positions of joints 610. In step 710, positionvector θ can be determined based on actuator position vector θ.sub.Ahaving elements corresponding to respective positions of actuators 640.Each position component θ.sub.i, for an index i from 1 to N isdetermined using Equation 2, which defines a system of equationsdefining the relationship between actuator positions and jointpositions. In Equation 2, θ.sub.1 to θ.sub.N are components of theposition vector θ of joints 610, and θ.sub.A1 to θ.sub.AM are componentsof the position vector θ.sub.A respectively in M actuators 640 thatarticulate joints 610. Each coefficient b.sub.IJ for index I=1 to N andindex J=1 to M generally corresponds to a coupling constant between anactuator J and a joint I. For example, a unit coupling constant forb.sub.IJ for a given I and a given J indicates that the position ofjoint I is considered to be directly proportional to the position ofactuator J. The matrix with components b.sub.IJ can be referred to ascoupling matrix C.

[θ 1 θ 2 .Math. θ N ] = [ b 11 .Math. b 1 .Math. M .Math.^(•)•_(•).Math. b N .Math..Math. 1 . Math. b NM ] [ θ A .Math..Math. 1 θA .Math..Math. 2 .Math. θ AM ] Equation .Math..Math .2

Control system 650 receives a surgeon’s instructions in step 715. Thesurgeon’s instructions can indicate a desired configuration of theinstrument, e.g., specifying a position and velocity of a specificworking portion of the instrument. For example, a surgeon throughmanipulation of manual control 660 can indicate a desired position,velocity, orientation, and rotation of the distal tip or end effector ofthe instrument such as described in U.S. Pat. No. 6,493,608, entitled“Aspects of a Control System of a Minimally Invasive SurgicalApparatus,” which is incorporated herein by reference.

Step 720 then converts the instructions from manual controller 660 intodesired position and velocity vectors θ.sub.D and {dot over (θ)}.sub.Dfor joints 610. For example, given the desired position, orientation,velocity, and angular velocity of the distal tip of instrument 600 ofFIG. 6 , control system 650 can calculate desired joint position andvelocity vectors θ.sub.D and {dot over (θ)}.sub.D that will achieve thedesired tip configuration. The conversion step 720 can be achieved withwell-known techniques, such as differential kinematics inversion asdescribed by “Modeling and Control of Robot Manipulators,” L. Sciaviccoand B. Siciliano, Springer, 2000, pp. 104-106 and “Springer Handbook ofRobotics,” Bruno Siciliano & Oussama Khatib, Editors, Springer, 2008,pp. 27-29, which are incorporated herein by reference. Above-referencedU.S. Pat. No. 6,493,608, entitled “Aspects of a Control System of aMinimally Invasive Surgical Apparatus,” also describes techniques fordetermining desired joint position and velocity vectors θ.sub.D and {dotover (θ)}.sub.D that will achieve the desired tip configuration. Itshould be noted that for instruments with a kinematic redundancy, i.e.,if the number of degrees of freedom of motion provided by joints 610 islarger than the number of degrees of freedom of the motion commandspecified by manual controller 660, the redundancy can be resolved withstandard techniques such as those described in Yoshihiko Nakamura,“Advanced Robotics: Redundancy and Optimization,” Addison-Wesley (1991).

It should also be appreciated that software enforced constraints betweenthe joints of the instruments can also be enforced when solving theinverse kinematics problem on the desired command for the instrument.For instance, the joint positions and velocity commands of two jointscan be forced to be the same or opposite or in a given ratio,effectively implementing a virtual cam mechanism between the joints. Thesoftware enforced constraints can include software enforced minimumtensions in the transmission systems of the instrument, maximum tensionsin the transmission systems of the instrument, etc. The softwareenforced constraints can be dynamically enforced during a surgicalprocedure. As desired positions, desired velocities, measured positions,and measured velocities vary, the software enforced constraints canvary.

Step 725 computes a position error vector (θ.sub.D-θ) and velocity errorvector ({dot over (θ)}.sub.D-{dot over (θ)}), and step 730 usescomponents of error vectors (θ.sub.D-θ) and ({dot over (θ)}.sub.D-{dotover (θ)}), for calculation of respective torque components τ.sub.1 toτ.sub.N. In one specific embodiment, each torque component τ.sub.i foran index i from 1 to N is determined using Equation 3. In Equation 3,g1.sub.i and g2.sub.i are gain factors, and C.sub.i is a constant orgeometry-dependent parameter that may be selected according to known ormodeled forces applied to the joint by other portions of the system.However, parameter C.sub.i is not required to strictly be a constant butcould include non-constant terms that compensate for properties such asgravity or mechanism stiffness that can be effectively modeled, andaccordingly, C.sub.i may depend on the measured position or velocity ofthe joint 610-i on which the torque

acts. In general, gain factors gl.sub.i and g2.sub.i and constantC.sub.i can be selected according to the desired stiffness and dampeningor responsiveness of a joint or according to an accumulation of error.For example, when inserting the instrument 600 to follow a natural lumenwithin a patient, the gain factor gl.sub.i can be set to a low value tomake a joint behave gently and prevent the joint action from harmingsurrounding tissue. After the insertion, the gain factor gl.sub.i can beset to a higher value that allows the surgeon to perform a precisesurgical task with the instrument. Other equations or corrections toEquation 3 could be employed in the determination of the torque. Forexample, the calculated torque could include a correction proportionalto a saturated integral of the difference between the currentmeasurement of joint position and the desired joint position that thepreviously applied torque was intended to achieve. Such correction usinga saturated integral could be determined as described above for thesingle joint control process of FIG. 5A and particularly illustrated bysteps 530 and 535 of FIG. 5A.

$\begin{array}{l}{\tau.\text{sub}\text{.i=}g1.\text{sub}\text{.i}\left( {\theta.\text{sub}\text{.D} - \theta} \right).\text{sub}\text{.i+}} \\{g2.\text{sub}\text{.i}\left( {\left\{ {\text{dot over}(\theta)} \right\}.\text{sub}\text{.D} - \left\{ {\text{dot over}(\theta)} \right\}\mspace{6mu}} \right).\text{sub}\text{.i+}C.\text{sub}\text{.i}}\end{array}$

Step 735 uses the torques computed in step 730 to determine distaltensions T.sub.DIST. Distal tension T.sub.DIST is an M component vectorcorresponding to transmission systems 620-1 to 620-M and actuators 640-1to 640-M. The determination of the distal tensions depends on geometryor mechanics between the instrument joints and transmission systems. Inparticular, with multiple joints, each joint may be affected not only bythe forces applied directly by transmission systems attached to thejoint but also by transmission systems that connect to joints closer tothe distal end of the instrument. The torques and tensions in a medicalinstrument can generally be modeled using equations of the form ofEquation 4. In Equation 4,

to

are components of the torque vector, and

to T.sub.M are the distal tensions respectively in M transmissionsystems 620 that articulate joints 610. Each coefficient au for index1=1 to N and index J=1 to M generally corresponds to the effectivemoment arm of the tension T.sub.J for joint and rotation axiscorresponding to torque

[τ 1 τ 2 .Math. τ N] = [ a 11 a 12 .Math. a 1 .Math. M a 21 a 22 .Math.a 2 .Math. M .M ath. .Math.

.Math. a N .Math..Math. 1 a N .Math..Math. 2 .Math. a NM] [ T 1 T 2.Math. T M ] = A

[ T 1 T 2 .Math. T M ] Equation .Math..Math. 4

The computation in step 735 thus corresponds to solving N equations forM variables T.sub.1 to T.sub.M. Since M is generally greater than N, thesolution is not unique, so that inequality constraints can be selected,such as the constraint that all tensions are greater than a set ofminimum values, and optimality conditions, such as the condition that aset of tensions of lowest maximum value is chosen, can be applied toprovide a unique solution with desired characteristics such as minimaltensions that stay above a desired threshold in all or selected joints.The matrix inversion problem of Equation 4 with inequality andoptimality constraints such as minimal tension constraints can be solvedby some well-known techniques such as the SIMPLEX method of linearprogramming. (See, e.g., “Linear Programming 1: Introduction,” George B.Dantzig and Mukund N. Thapa, Springer-Verlag, 1997, which isincorporated herein by reference in its entirety.) In accordance with afurther aspect of the invention, the distal tensions can be determinedusing a process that sequentially evaluates joints beginning with themost distal joint and solves for tensions in transmission systems thatconnect to each joint based on geometric parameters and the tensionspreviously calculated for more distal joints.

In some cases, the distal tensions T.sub. 1 to T.sub.M to be applied aredirectly proportional to actuator torques τ.sub.A1 AN to T.sub.AN to beapplied by actuators 640. In this regard, in some cases, at step 735,actuator torques T.sub.A1 to T.sub.AN are determined. In Equation 5

each coefficient d.sub.JI of coupling matrix D for index I =1 to N andindex J =1 to M generally corresponds to the torque coupling between ajoint I and an actuator J. If position vector θ of joints 610 isdetermined based on Equation 2, the relationship between torques τ.sub.1to T.sub.N (represented by torque vector τ) and torques τ.sub.A1 toτ.sub.AM (represented by torque vector τ.sub.A) to be applied byactuators 640 can be determined based on the coupling matrix C. Couplingmatrix D relating the torque vector τ and the torque vector τ.sub.A canbe equal to the transpose of coupling matrix C. With Equation 5, at step735, the torques τ.sub.A1 to τ.sub.AM to be applied to actuators 640 canbe determined given joint torques τ.sub.1 to τ.sub.N, for example,calculated using Equation 3.

[ τ A .Math. .Math. 1 τ A .Math. .Math. 2 .Math. τ AM ] = [d 11 .Math. d1 .Math. N .M ath.

.Math. d M .Math..Math. 1 .Math. d MN ]

[ τ 1 τ 2 .Math. τ N ] Equation .Math..Math. 5

Control system 650 in one embodiment of process 700 activates actuators640. As described with respect to step 735, distal tensions to beapplied to transmission system 620 or torques to be applied to actuators640 can be determined. Actuators 640 can be activated to apply thedistal tensions or the torques calculated in step 735 to respectivetransmission systems 620.

Alternatively, corrections to the distal tensions can be determined asillustrated by steps 740 and 745. In particular, step 740 computes acorrection tension T.sub.PROX, which depends on the difference between adesired transmission velocity vector {dot over (θ)} .sub.DL, computedbased on desired joint velocity {dot over (θ)}.sub.D, and a currenttransmission velocity vector θ.sub.L, computed based on the currentactuator velocity {dot over (θ)} .sub.A. In one particular embodiment,the desired transmission velocity can be the multiplication of thetranspose of the coupling matrix A in Equation 4 with the desired jointvelocity {dot over (θ)}.sub.D, while the current transmission velocitycan be the product of the actuator velocity {dot over (θ)}.sub.A andrespective moment arm of actuators 640. Correction tension T.sub.PROXcan compensate for inertia or other effects between the actuator 640 andthe connected joint 610 and, in one embodiment, is a function of thedifference ({dot over (θ)}.sub.DL- {dot over (θ)}.sub.L) such as theproduct of difference ({dot over (θ)}.sub.DL- {dot over (θ)}.sub.L)and again factor. Step 745 computes a correction tension T.sub.PAIR, whichdepends upon a difference or differences between the velocities ofactuators that actuate the same j oint. For example, in the case inwhich a joint provides one degree of freedom of motion and is actuatedby a pair of actuators connected to the joint through a pair oftransmission systems, correction tension T.sub.PAIR can be determined asa function of the difference between the velocities of the twoactuators. (See, for example, step 550 of FIG. 5A as described above.)Corrections similar to correction tension T.sub.PAIR can be generalizedto the case where three or more transmission systems and actuatorsactuate a joint having two degrees of freedom of motion.

Step 750 combines distal tension T.sub.DIST and any correctionsT.sub.PROX or T.sub.PAIR to determine a combined tension T applied bythe actuators. In general, each component T.sub.1 to T.sub.M of thecombined tension T can be limited to saturate at a maximum tensionT.sub.MAX or a minimum tension T.sub.MIN if the sum of the calculateddistal tensions T.sub.DIST and corrections T.sub.PROX and T.sub.PAIR isgreater than or less than the desired maximum or minimum values asdescribed above with reference to FIG. 5D. As a result, all tensionsT.sub. 1 to T.sub.M are no less than a minimum tension T.sub.MIN or nogreater than a maximum tension T.sub.MAX. Steps 755 and 760 thenactivate actuators 640 to apply and hold the combined tension T for atime interval Δt before process 700 returns to step 710 and reads thenew joint positions. Holding the tension for an interval of roughly 4 msor less, which corresponds to a rate of 250 Hz or higher, can providesmooth movement of an instrument for a medical procedure. In someimplementations, time interval Δt is 0.1 ms to 4 ms, e.g., 0.1 ms to 1ms, 1 ms to 2 ms, 2 ms to 3 ms, or 3 ms to 4 ms.

Medical instruments commonly require that the working tip or endeffector of the instrument have a position and orientation that anoperator such as a surgeon can control. On the other hand, the specificposition and orientation of each joint is generally not critical to theprocedure being performed, except where joint position or orientation ismandated by the lumen through which the instrument extends.

In accordance with an aspect of the invention, one approach to control amulti joint instrument selects tensions applied through tendons usingdifferences between current and desired configurations of an end portionof an instrument, e.g., such as an end effector, a tip, or other movabledevice. For example, differences between the measured position,orientation, velocity, and angular velocity of the end portion of theinstrument and the desired position, orientation, velocity, and angularvelocity of the end portion of the instrument can control the tensionsapplied to tendons of a medical instrument. FIG. 7B illustrates acontrol process 700B in accordance with an embodiment of the invention.

Process 700B employs some of the same steps as process 700, and thosesteps have the same reference numbers in FIGS. 7A and 7B. Process 700Bin step 710 determines the joint positions θ and joint velocities {dotover (θ)}, for example, from a sensor or sensors. As described herein,the sensor or sensors can include distal sensors or proximal sensors. Instep 712, process 700B reads or determines a position, orientation,velocity, and angular velocity of a tip of the instrument. Tip hererefers to a specific mechanical structure in the instrument and may bean end effector such as forceps, scissors, a scalpel, or a cauterizingdevice on the distal end of the instrument. In some examples, an endportion of the instrument includes the tip. In general, the tip has sixdegrees of freedom of motion and has a configuration that can be definedby six component values, e.g., three Cartesian coordinates of a specificpoint on the tip and three angles indicating the pitch, roll, and yaw ofthe tip. Velocities associated with changes in the configurationcoordinates over time may be directly measured or calculated usingmeasurements at different times. Given j oint positions and velocities θand {dot over (θ)} and a priori knowledge of the kinematic model of theinstrument 600, one can build both forward and differential kinematicmodels that allow computing the Cartesian position, orientation,translational velocity, and angular velocity of the tip with respect tothe frame of reference of the instrument 600. The forward anddifferential kinematic model of a kinematic chain can be easilyconstructed according to known methods. For instance, the proceduredescribed by John J. Craig, “Introduction to Robotics: Mechanics andControl,” Pearson Education Ltd. (2004), which is incorporated herein byreference, may be used. Step 715 determines the desired tip position,orientation, translational velocity, and angular velocity, which can beperformed in the manner described above. The desired tip position,orientation, translational velocity, and angular velocity may becomputed using kinematic models similar to those described herein withrespect to computing configurations of instrument 600.

In another embodiment, a sensor, for example, a shape sensor, may beused to directly measure Cartesian position and orientation as describedin U.S. Pat. App. Pub. No. 20090324161 entitled “Fiber optic shapesensor” by Giuseppe M. Prisco, which is incorporated herein byreference. Translational velocities associated with changes in theconfiguration coordinates over time may be calculated using measurementsat different times. Unlike the translational velocities, the angularvelocities cannot be computed simply by the differencing approach due tothe angular nature of the quantities. However, the methods of computingthe angular velocities associated with the changes in orientation areknown in the art and described, for example, by L. Sciavicco and B.Siciliano, “Modelling and Control of Robot Manipulators,” Springer 2000,pp. 109-111.

Process 700B in step 722 calculates tip errors. The tip errors areindicative of a difference between a current configuration of the tipand a desired configuration of the tip. In one embodiment, step 722includes calculating a position error or difference epos between thedesired Cartesian coordinates of the tip and the current Cartesiancoordinates of the tip, a translational velocity error or differencee.sub.VT between the desired translational velocity of the tip and thecurrent translational velocity of the tip, an orientation error ordifference e.sub.ORI between the desired orientation coordinates of thetip and the current orientation coordinates of the tip, and an angularvelocity error or difference e.sub.VA between the desired angularvelocity of the tip and the current angular velocity of the tip. Unlikethe position error e.sub.POS, the orientation error e.sub.ORI cannot becomputed simply by the differencing approach due to the angular natureof the quantities. However, the methods of computing the change inorientation are known in the art and can be found in roboticsliteratures, for example, L. Sciavicco and B. Siciliano, “Modelling andControl of Robot Manipulators,” Springer, 2000, pp. 109-111.

In step 724, process 700B determines a tip force F.sub.TIP and a tiptorque τ.sub.TIP that are intended to move tip from the currentconfiguration to the desired configuration. In this embodiment of theinvention, tip force F.sub.TIP depends on errors e.sub.POS and e.sub.VT.For example, each component F.sub.X, F.sub.Y, or F.sub.Z of tip forceF.sub.TIP can be calculated using Equation 6, where gp.sub.i andgv.sub.i are gain factors and Cƒ.sub.i is a constant. The tip torqueτ.sub.TIP can be determined in a similar manner, in which each componentof tip torque τ.sub.i is a function of errors e.sub.ORI and e.sub.VAwith another set of gain factors and constants gori.sub.i, gva.sub.i,and Cτ.sub.i as shown in Equation 7. In general, the gain factorsgp.sub.i and gv.sub.i associated with different force or torquecomponents F.sub.i and τ.sub.i can be different. Having separate gainfactors and constants for each component of tip force F.sub.TIP and tiptorque τ.sub.i provides flexibility in specifying the dynamic behaviorof the end effector or instrument tip, enhancing more effectiveinstrument interaction with the tissue. For instance, when navigatingthe instrument into a small lumen, one may set low values for the gainfactors of tip force perpendicular to the inserting direction while havehigh values for the gain factors along the inserting direction. Withthat, the instrument is sufficient stiff for insertion while having lowlateral resistance to the tissue, preventing damage to the surroundingtissue. Another example, when using the instrument to punch a hole inthe tissue in certain direction, having high values in the gain factorsof the tip torque as well as the gain factor along the insertingdirection of the tip force, facilitate the hole-punch task.

F.sub.i=gp.sub.i*e.sub.POS+gv.sub.i*e.sub.VT+Cf.sub.i

τ.sub.i=gori.sub.i*e.sub.ORI+gva.sub.i*e.sub.VA+Cτ.sub.i

Step 732 determines a set of joint torques that will provide the tipforce F.sub.TIP and tip torque τ.sub.TIP determined in step 724. Therelationships between joint torque vector τ, tip force F.sub.TIP, andtip torque τ.sub.TIP are well-documented and normally described as inEquation 8, where J.sup.T is the transpose of the well-known JacobianMatrix J of a kinematic chain of the instrument.

$\tau = \text{J}\mspace{6mu}\text{T}\boxed{}\mspace{6mu}\left\lbrack {\mspace{6mu}\text{F TIP}\tau\mspace{6mu}\text{TIP}\mspace{6mu}} \right\rbrack\mspace{6mu}\text{Equation}\mspace{6mu}\text{.Math}\text{.}\mspace{6mu}\text{.Math}\text{.}\mspace{6mu}\text{8}$

The Jacobian Matrix J depends on the geometry of the instrument and thecurrent joint positions determined in step 710 and can be constructedusing known methods. For example, John J. Craig, “Introduction toRobotics: Mechanics and Control,” Pearson Education Ltd. (2004), whichis incorporated herein by reference, describes techniques that may beused to construct the Jacobian Matrix for a robotic mechanism. In somecases, if there are extra or redundant degrees of freedom of motionprovided in the medical instrument, e.g., more than the six degrees offreedom of motion of the tip, the set of joint torques that provides tipforce F.sub.TIP and tip torque τ.sub.TIP is not unique, and constraintscan be used to select a set of joint torques having desired properties,e.g., to select a set of joint torques that prevents the joints reachingtheir mechanical joint limits in range of motion or supported loads orto enforce extra utility on any particular joints of the instrumentduring manipulation. For instance, one can prevent the joints reachingtheir mechanical joint limits by selecting a set of j oint torques thatminimizes the deviation from the midrange joint positions, from the nullspace associated with the transpose of Jacobian matrix J.sup.T. The setof joint torques can be selected according to Equation 9. In Equation 9,P(θ) is a potential function that define addition utility to be providedby the solution, ∇ is a gradient operator, N () is a null spaceprojection operator that selects a set of joint torques from the nullspace of the transpose of Jacobian matrix J.sup.T, associated with itsinput. In one embodiment, potential P(θ) a quadratic function of thejoint positions that has a minimum when the joints are in the center oftheir range of motion. The gradient of the potential function -∇P(θ)selects a set of joint torques that draws joints moving toward thecenter of their range of motion while the null space projection operatorN () enforces that the selected set of joint torques providing thedesired tip force and tip torques also satisfy the additional utility.Techniques for using constraints in robotic systems providing redundantdegrees of freedom of motion are known in the art and can be found inrobotics literatures. See, for instance, Yoshihiko Nakamura, “AdvancedRobotics: Redundancy and Optimization,” Addison-Wesley (1991) andliterature by Oussama Khatib, “The Operational Space Framework,” JSMEInternational Journal, Vol. 36, No. 3, 1993.

τ = JT▫[F TIP τ TIP] + N▫(−∇P▫(θ))Equation .Math. .Math. 9

Process 700B after step 732 proceeds in the same manner as process 700described above. In particular, based on the joint torques determined instep 732, step 735 determines tensions T.sub.DIST. Steps 740 and 745determine corrections T.sub.PROX and T.sub.PAIR to tensions T.sub.DIST,and step 750 determines a combined tension vector T. Steps 755 and 760then apply and hold the components of combined tension vector T on thetransmission systems to actuate the medical instrument during a timeinterval Δt.

Processes 700 and 700B of FIGS. 7A and 7B required determination oftensions that will produce a particular set of joint torques. The tendontension for a single isolated joint can be determined from a j ointtorque simply by dividing the j oint torque by the moment arm at whichthe tension is applied. In the multi joint case, due to geometry of thetransmission system and cable routing and redundancy in the actuationcable, the problem amounts to solving a system of equations withconstraints. In one particular embodiment, one may apply non-negativetendon tension constraints (or minimum tension constraints) when solvingthe system of equations to prevent slacking in the cables or othertendons in the transmission systems. The inputs of the problem are thedetermined j oint torque for each j oint while the geometry of cablerouting defines the system of equations (or the coupling matrix A ofEquation 4). Appropriate tendon tensions are needed that fulfillEquation 4 and are larger than minimum tension constraints.

In some examples, a standard optimization method, called SIMPLEX methodcan be used to handle this matrix inverse problem with inequality andoptimality constraints. The SIMPLEX method can require a relativelylarger computation time and may not be advantageous to be used in realtime application. Also, the SIMPLEX method does not guarantee continuityin the solutions as the joint torques change. To speed-up thecomputation efficiency and provide a continuous output solution, aniterative approach can be considered which relies on the triangularnature of the coupling matrix A. FIGS. 8A, 8B, 8C, 9A, 9B, 9C, 9D, and9E illustrate a few specific examples of joints in multi jointedinstruments and are used herein to illustrate some properties of thecoupling matrix A in Equation 4.

Various constraints can be enforced using the optimization methodsdescribed herein. If the number of actuators M is greater than thenumber of joints N, one of the redundant degrees of freedom ofinstrument 600 can be utilized to enforce a minimum tension T.sub.MIN.In some examples, a minimum tension T.sub.MIN can be enforced such thatthe tension in each of each transmission system 620 is greater than orequal to minimum tension T.sub.MIN. Torques

to

to be applied can be selected to enforce minimum tension T.sub.MIN ineach transmission system 620. In this regard, the actuator torques

to

can each be biased by a certain amount of tension to achieve suchtensions above minimum tension T.sub.MIN. Actuators 640 can becontrolled to apply tensions to transmission systems 620 both based onthe position and velocity errors and based on offset tensions that causethe applied tensions to be no less than minimum tension T.sub.MIN. Thiscan inhibit slack in transmission systems 620, e.g., during a surgicalprocedure, thereby improving responsiveness of instrument 600.

In some examples, offset tensions are provided by a parameter that isindependent of positions of joints 610 so that variation in theparameter does not influence net torques on joints 610 and thus does notinfluence positioning of joints 610. The parameter is dependent onpositions of actuators 640. As a result, actuators 640 can be driven tomaintain a particular value for the parameter or a particular range ofvalues for the parameter without affecting joint torques. If actuators640 are controlled based on determined torques τ to τ sub.AM, a biasparameter τBIAS can be selected to offset torques applied by actuators640 and hence to offset tensions applied to transmission systems 620.Bias parameter τ.sub.BIAS thus provides the offset tensions applied totransmission systems 620. Absent bias parameter τ.sub.BIAS (e.g., whenbias parameter τBIAS is equal to zero), resulting baseline tensionsapplied to transmission systems 620 are based only on position errors ofjoints 610 and not based on the offset tensions or otherconstraint-based tensions. With a non-zero value for bias parameterτ.sub.BIAS, resulting tensions applied to transmission systems 620 arebased on position errors of joints 610 and based on the offset tensions.

A selected bias parameter τ.sub.BIAS can provide a corresponding offsettension for each of tensions T.sub.l to T.sub.M. For example, in somecases, multiple offset tensions are equal to one another. Alternativelyor additionally, multiple offset tensions are different from oneanother. In some cases, all of the offset tensions are equal to oneanother, and in other cases, none of the offset tensions are equal toone another.

By way of example, bias parameter τ.sub.BIAS can form part of a systemof equations to provide the offset tensions. The system of equations,including equations relating joint positions and actuator positions, isaugmented to include an additional equation that functions as aconstraint on tensions T.sub.1 to T.sub.M of transmission systems 620.This additional equation provides the offset tensions that bias theapplied tensions T.sub.1 to T.sub.M to be no less than minimum tensionT.sub.MIN. For example, this additional equation is defined by arelationship between θ.sub.T representing a tension degree of freedom(in Equation 2A below) and actuator positions θ.sub.A1 to θ.sub.AM.While θ.sub.1 to θ.sub.N correspond to physical positions of joints 610,θ.sub.T corresponds not to a physical position of a joint but rather atension degree of freedom θ.sub.T that is adjustable to causecorresponding tensions in transmission systems 620. Equation 2A(θ=Cθ.sub.A) corresponds to Equation 2 augmented by an additionalequation usable to enforce minimum tension T.sub.MIN, as represented bycoefficients b.sub.T1 to b.sub.TM and variable θ.sub.T. The matrix Ccorresponds to the full matrix of Equation 2 with additionalcoefficients b.sub.T1 to b.sub.TM for tension degree of freedom θ.sub.T.Components of matrix C are selected such that at least one column islinearly independent of the others, e.g., the column corresponding tothe tension degree of freedom θ.sub.T. This linear independence canensure that enforcement of the minimum tension constraint does not causecorresponding changes to positions of the joints or a net torque appliedto the joints. For example, the linear independence ensures thatpositions θ.sub.1 to θ.sub.N remain unchanged in response to changes inthe tension degree of freedom θ.sub.T.

[ θ 1 θ 2 .Math. θ N θ T ] = [ b 11 .Math. b 1 .Math. M .Math. ^(•)•_(•).Math. b N .Math..Math . 1 b NM .Math. b T .Math..Math. 1 b TM ]

[ θ A .Math..Math. 1 θ A .Math..Math. 2 .Math. θ AM ] Equation.Math..Math. 2 .Math. A

The relationship between actuator torques

.sub.A1 to

ub.AM to be applied and joint torques τ.sub.1 to τ.sub.N can berepresented by Equation 5A. As described above, matrix D havingcoefficients d.sub. 11 to d.sub.MN for index I=1 to N and index J=1 to Mcan be determined by taking the transpose of coupling matrix C ofEquation 2A. The bias parameter τ.sub.BIAS can be selected to provideoffset tensions that cause each of actuator torques τ.sub.A1 to τ.sub.AMto be applied to be greater than minimum torque τ.sub.MIN, e.g.,corresponding to minimum tension T.sub.MIN.

As shown in Equation 5A, applied actuator torques τ.sub.A1 to τ.sub.AMcan be equal to the sum of baseline torques and bias torques. Thebaseline torques correspond to the torques to be applied to actuators640 absent the minimum tension constraint. Both the baseline torques andapplied actuator torques τ.sub.A1 to τ.sub.AM result in tensions appliedto transmission systems 620 that reduce the difference between thecurrent configuration and the desired configuration. Said another way,the baseline torques and actuator torques τ.sub.A1 to τ.sub.AM, whenapplied, generate a desired net torque at joints 610. The bias torquescorrespond to the additional torques to be applied to actuators 640 toensure that actuator torques τ.sub.A1 to τ.sub.AM is each greater thanminimum torque T.sub.MIN. The bias torques do not influence the currentconfiguration. Said another way, the bias torques, when applied totransmission systems 620, provide the offset tensions to transmissionsystems 620 and generate a zero net torque at joints 610. The biastorques provide offset tensions to transmissions systems 620 such thatan average of the tensions experienced by transmission systems 620 ismaintained. Accordingly, the net torque on joints 610 is not affected bythe offset tensions.

In some examples, using Equation 5A, bias parameter τ.sub.BIAS can bethe minimum value required such that each of torques τ.sub.A1 toτ.sub.AM is greater than minimum torque τ.sub.MIN. In an example of aprocess to select a minimum value of bias parameter τ.sub.BIAS, for eachactuator torque τ.sub.A1 to τ.sub.AM, an offset torque added to thebaseline torque is determined. For each actuator torque τ.sub.A1 toτ.sub.AM, the corresponding offset torque is determined so that theactuator torque is greater than minimum torque τ.sub.MIN. A maximum ofthese added torques is used to determine bias parameter τ.sub.BIAS suchthat each of torques τ.sub.A1 to τ.sub.AM is greater than minimum torqueτ.sub.MIN. This ensures that bias parameter τ.sub.BIAS is its minimumrequired value to enforce the minimum tension and torque constraint. Asa result, by enforcing minimum torque τ.sub.MIN, one or more of torquesτ.sub.A1 to τ.sub.AM is equal to minimum torque τ.sub.MIN, and aremaining of torques τ.sub.A1 to τ.sub.AM is greater than minimum torqueτ.sub.MIN. In some cases, multiple torques of torques τ.sub.A1 toτ.sub.AM are equal to minimum torque τ.sub.MIN. In particular, torquesτ.sub.A1 to τ.sub.AM are selected to inhibit slack in all of thetransmission systems 620 and to maintain tensions in transmissionsystems 620 above minimum tension T.sub.MIN.

[ τ A .Math..Math. 1 τ A .Math..Math. 2 .Math. τ AM ] = [ d 11 .Math. d1 .Math. N d 1 .Math. T .Math. ^(•)•_(•) .Math. .Math. d M .Math..Math.1 .Math. d MN d MT ] baseline .Math. [τ 1 τ 2 .Math. τ N 0 ] + [ d 11.Math. d 1 .Math. N d 1 .Math. T .Math. .Math..Math. d M .Math. .Math. 1.Math. d MN d MT ] bias □[ 0 0 .Math. 0 τ BIAS ] Equation .Math..Math. 5.Math. A

In some implementations, bias parameter τ.sub.BIAS is dynamically variedduring the surgical procedure as the required bias torques to achievetensions no less than minimum tension T.sub.MIN vary due to changes indesired and measured positions, velocities, and/or torques of the joints610 and actuators 640. In this regard, bias parameter τ.sub.BIAS can bevaried at each measurement interval. When bias parameter τ.sub.BIAS isdynamically varied, while tensions in transmission systems 620 may varybetween measurement intervals, an average of tensions in transmissionsystems 620, e.g., a mean of the tensions in transmission systems 620,is maintained between different measurement intervals. The bias torquesprovide offset tensions to transmissions systems 620 such that theaverage of the tensions experienced by transmission systems 620 ismaintained.

Torques τ.sub.A1 to τ.sub.AM, adjusted by bias parameter τ.sub.BIAS, areapplied to generate corresponding tensions T.sub.1 to T.sub.M intransmission systems 620. Values of each of tensions T.sub.1 to T.sub.Mcan increase due to increases in bias parameter τ.sub.BIAS. As a result,adjustment of actuator torques τ.sub.A1 to τ.sub.AM using bias parameterτ.sub.BIAS can result in higher tensions T.sub.1 to T.sub.M. Even ifbias parameter τ.sub.BIAS is selected to be its minimum required value,bias parameter τ.sub.BIAS may continue to increase due to slack in onetransmission system, thereby causing high values for tensions for othertransmission systems. For example, to achieve a desired configuration ofjoints 610, a first of transmission systems 620 can be driven to ahigher value of tension while a second of transmission systems 620 isreleased to a lower value of tension. The tension in the secondtransmission system 620 can decrease to an extent that, inimplementations in which bias parameter τ.sub.BIAS is dynamicallycontrolled, bias parameter τ.sub.BIAS is increased to maintain thetension in the second transmission system 620 above the minimum tensionT.sub.MIN. As a result, the first transmission system 620 may experienceincreases in tension due to the increase in bias parameter τ.sub.BIAS.

An example process 1100 in which offset tensions are dynamically variedis described herein with respect to FIG. 11 . In addition, furtherexamples of enforcing a nominal tension other than a minimum tensionT.sub.MIN for a transmission system is described with respect to process1100 of FIG. 11 herein. In these examples, bias parameter τ.sub.BIAS canbe used to enforce the nominal tension.

Rather than being dynamically controlled, bias parameter τ.sub.BIAS maybe statically controlled during a portion of the surgical procedure orduring an entire surgical procedure so that bias parameter τ.sub.BIAS ismaintained at a particular desired value even if tensions in one or moreof transmission systems 620 decreases to values below minimum tensionT.sub.MIN. For example, bias parameter τ.sub.BIAS can be staticallycontrolled to avoid large tensions in transmission systems 620 that canincrease a likelihood of damaging transmission systems 620.

A statically controlled bias parameter τ.sub.BIAS provides constantoffset tensions that are independent of current tensions of transmissionsystems 620, and are also independent of current positions of joints610. The resulting offset tensions can offset tensions of thetransmission systems 620 by different amounts or by the same amount. Forexample, in some cases, two or more of the constant offset tensions areequal to one another. In some cases, two or more of the constant offsettensions are different from one another. Some of the constant offsettensions may be equal to another, while some of the constant offsettensions may differ from one another.

In such examples, rather than dynamically varying bias parameterτ.sub.BIAS such that bias parameter τ.sub.BIAS varies at eachmeasurement interval, bias parameter τ.sub.BIAS is selected for aparticular measurement interval and the selected bias parameterτ.sub.BIAS is applied for one or more subsequent measurement intervals.In the one or more subsequent measurement intervals, bias parameterτ.sub.BIAS remains set at the initial value selected at the particularmeasurement interval. The offset tensions provided by the selected biasparameter τ.sub.BIAS thus remain the same during the one or moresubsequent measurement intervals even if one or more of current tensionsT.sub.1 to T.sub.M falls below minimum tension T.sub.MIN. While currenttensions T.sub.1 to T.sub.M may be increased or decreased in response toachieve the desired configuration for joints 610, the constraint toenforce minimum tension T.sub.MIN only causes changes to tensionsT.sub.1 to T.sub.M during the particular measurement interval, notduring the one or more subsequent measurement intervals.

Alternatively, bias parameter τ.sub.BIAS is selected and maintained foran entire surgical procedure. In some examples, bias parameterτ.sub.BIAS is selected based on a number of uses of instrument 600. Ifinstrument 600 is a multi-use instrument, each use of instrument 600 canalter characteristics of transmission systems 620. For example, ifinstrument 600 includes springs or other mechanical devices to provideoffset tensions to transmission systems 620, these mechanical devicescan relax over multiple uses of instrument 600. The software-enforcedoffset tensions provided by bias parameter τ.sub.BIAS can increase aftereach use in response to relaxation of the hardware-enforced offsettensions.

In some examples, bias parameter τ.sub.BIAS is selected based on atorque range for instrument 600 during a medical operation, or a rangeof motion for joints 610 during the medical operation. For example, forsmaller torque ranges or smaller ranges of motion, e.g., less than 50%,less than 40%, or less than 30% of the entire ranges of motions forjoints 610, bias parameter τ.sub.BIAS can be selected to provide greaterconstant offset tensions such that smaller manipulations of joints 610can be more easily achieved. In particular, greater constant offsettensions can increase responsiveness of transmission systems 620 andhence allow for torque provided by actuators 640 to more easily transferto joints 610.

In some implementations, rather than being controlled statically ordynamically for an entirety of a surgical procedure, bias parameterτ.sub.BIAS can be controlled in a hybrid manner in which bias parameterτ.sub.BIAS is statically controlled for a portion of the surgicalprocedure and dynamically controlled for another portion of the surgicalprocedure. For example, bias parameter τ.sub.BIAS can be controlleddynamically in accordance to the process described herein with respectto Equation 5A when tensions T.sub.1 to T.sub.M are each less than orequal to a predefined threshold tension. Bias parameter τ.sub.BIAS canbe controlled statically when one or more of tensions T.sub.1 to T.sub.Mare greater than or equal to the predefined threshold tension. Forexample, the bias parameter τ.sub.BIAS is maintained at a constantpredefined value when one or more of tensions T.sub.1 to T.sub.M aregreater than or equal to the threshold tension. In such cases, biasparameter τ.sub.BIAS is variable when tensions in transmission systems620 are each less than or equal to the threshold tension, bias parameterτ.sub.BIAS is fixed when tension in one or more of transmission systems620 is greater than or equal to the threshold tension. In particular,bias parameter τ.sub.BIAS is varied depending on the tensions intransmission systems 620 when bias parameter τ.sub.BIAS is variable, andis fixed at a predefined value regardless of values of tensions intransmission systems 620 when bias parameter τ.sub.BIAS is fixed. Inthis hybrid approach, at lower tensions, the dynamic control of biasparameter τ.sub.BIAS can inhibit one or more of transmission systems 620from becoming slack. At higher tensions, the static control of biasparameter τ.sub.BIAS can reduce the likelihood that tensions T.sub.1 toT.sub.M increase to levels that can damage the transmission systems 620.

Alternatively, when controlled in the hybrid manner, bias parameterτ.sub.BIAS can be controlled dynamically in accordance to the processdescribed herein with respect to Equation 5A when tensions T.sub. 1 toT.sub.M are each greater than or equal to a predefined thresholdtension. As described herein, bias parameter τ.sub.BIAS can be used toenforce a nominal tension other than a minimum tension T.sub.MIN. Forexample, the nominal tension could be a maximum tension T.sub.MAX. Biasparameter τ.sub.BIAS can be controlled statically when one or more oftensions T.sub.1 to T.sub.M are less than or equal to the predefinedthreshold tension. For example, the bias parameter τ.sub.BIAS ismaintained at a constant predefined value when one or more of tensionsT.sub.1 to T.sub.M are less than or equal to the threshold tension. Insuch cases, bias parameter τ.sub.BIAS is variable when tensions intransmission systems 620 are each greater than or equal to the thresholdtension, bias parameter τ.sub.BIAS is fixed when tension in one or moreof transmission systems 620 is less than or equal to the thresholdtension. In this hybrid approach, at higher tensions, the dynamiccontrol of bias parameter τ.sub.BIAS can inhibit one or more oftransmission systems 620 from exceeding a certain maximum tensionT.sub.MAX. At lower tensions, the static control of bias parameterτ.sub.BIAS can increase the stiffnesses of transmission systems byapplying constant offset tensions.

In some implementations, a parameter for enforcing minimum torqueτ.sub.MIN, minimum tension T.sub.MIN, or other nominal tension ismonitored for error detection. For example, the parameter can correspondto bias constant τ.sub.BIAS or tension degree of freedom θ.sub.T. Inexamples in which tension degree of freedom θ.sub.T is monitored forerror detection, variation in tension degree of freedom θ.sub.T can beindicative of one or more faults associated with one or more oftransmission systems 620. For instance, because this parameter isdependent on positions of actuators 640 but is independent of positionsof joints 610, positions of actuators 640 can vary without acorresponding change in positions of joints 610 if transmission systems620 are faulty and not transferring force from actuators 640 to joints610. Accordingly, tension degree of freedom θ.sub.T being greater thanor equal to a predefined threshold value can be indicative of a faultassociated with transmission systems 620. For example, the fault maycorrespond to one or more of transmission systems 620 including a brokentendon or other faulty force transfer member. When transmission systems620 experience faults, tension degree of freedom θ.sub.T can increase toa value greater than or equal to the predefined threshold value. Forexample, in cases in which encoders are used to determine positions ofjoints 610, positions of joints 610 are not directly measured andpositions of actuators 640 are used to determine positions of joints610. As a result, when transmission systems 620 experience faults,actuators 640 are repositioned to drive transmission systems 620 eventhough this repositioning of the actuators 640 does not causerepositioning of joints 610. Actuators 640 are thus repositioned todrive transmission system 620 without causing a corresponding change inpositions of joints 610 that would be expected if transmission systems620 were functioning properly. Actuators 640 continue to be driven toattempt to achieve the desired configuration, and because the desiredconfiguration cannot be achieved, actuators 640 are driven such thattension degree of freedom θ.sub.T continues to increase.

In response to tension degree of freedom θ.sub.T being greater than orequal to the predefined threshold value, control system 650 controls auser output device, e.g., a speaker, a display, a vibration device, orother device that can provide audible, visual, or tactile feedback, togenerate an alert to provide feedback to the operator. In addition,control system 650 can cease driving of actuators 640 until the fault oftransmission systems 620 is addressed.

In some implementations, rather than issuing the alert in response to avalue tension degree of freedom θ.sub.T being greater than or equal tothe predefined threshold value, the control system 650 issues the alertin response to a rate of change of tension degree of freedom θ.sub.Tbeing greater than or equal to the predefined threshold value. The rateof change can increase rapidly when transmission systems 620 are brokenbecause transmission systems 620, when broken, do not provide resistancethat actuators 640 would otherwise have to drive against in order toreposition joints 610. Furthermore, because joints 610 cannot achievethe desired configuration when actuators 640 are driven, control system650 can continue to drive actuators 640, thereby causing the value ofand the rate of change of tension degree of freedom θ.sub.T to increase.Monitoring these values and providing alerts when they are greater thanor equal to predefined values can ensure that faults associated withtransmission systems 620 can be detected.

While the process associated with Equation 5A controls bias torquesbased on positions of actuators 640 and positions of joints 610, in someimplementations, actuator torques τ.sub.A1 to τ.sub.AM and transmissionsystem tensions T.sub.1 to T.sub.M are selected based on a dampingfunction. One or more of the current velocities of actuators 640 isdetermined. Based on the one or more current velocities, a dampingfunction is determined. The damping function is defined by one or moreparameters such as a damping coefficient, a natural frequency, or otherappropriate parameters that can be used to provide a dampening effect onmovement of actuators 640 and joints 610. The damping function isselected to inhibit sudden changes in positions of actuators 640 andaccordingly inhibit sudden changes in movement of joints 610. Thedamping function can be introduced to reduce tensions when actuators 640are operated at high velocities. For example, in situations whenactuators 640 are driven in one direction and then quickly driven in adifferent direction or are driven such that stiffnesses of transmissionsystems 620 are quickly reduced, the quick change in actuator motion cancause cables or tendons of transmission systems 620 to go slack. Thiscan cause the cables or tendons to unwind from actuators 640. Thedamping function can be introduced to prevent this from occurring.

FIG. 8A, for example, illustrates a portion of an instrument thatincludes multiple mechanical joints 810, 820, and 830. Each joint 810,820, or 830 provides a single degree of freedom, which corresponds torotation about an axis z1, z2, or z3 of the joint. In FIG. 8A, tendonsC1 and C2 connect to joint 810 for actuation of joint 810. Tendons C3and C4 pass through joint 810 and connect to joint 820 for actuation ofjoint 820. Tendons C5 and C6 pass through joints 810 and 820 and connectto joint 830 for actuation of joint 830. The proximal ends (not shown)of tendons C1 to C6 can be connected though compliant transmissionsystems such as illustrated in FIGS. 2 or 3A to respective drive motorsor other actuators. The control system for the instrument controls theactuators to apply respective tensions T1, T2, T3, T4, T5, and T6 intendons C1, C2, C3, C4, C5, and C6.

Joint 830 is at the distal end of the instrument in the illustratedembodiment, and actuation of joint 830 could be controlled using asingle-joint process such as described above with reference to FIGS. 5A,5B, 5C, and 5D. However, the total torque on joint 820 depends not onlyon the tensions in cables C3 and C4 but also the torque applied bytendons C5 and C6, which are connected to joint 830. The total torque onjoint 810 similarly depends not only on the tensions in tendons C1 andC2 but also the torque applied by tendons C3, C4, C5, and C6, which areconnected to joints 820 and 830 that are closer to the distal end.Models based on the geometric or kinematic characteristics of theinstrument can be developed to relate the torques τ1, τ2, and τ3 onjoints 810, 820, and 830 to the tension in tendons T1, T2, T3, T4, T5,and T6. Equation 4A illustrates one such mathematical model and providesa specific example of Equation 4 above. In Equation 4A, τ.sub.1,τ.sub.2, and τ.sub.3 are the respective actuating torques on joints 810,820, and 830, τ.sub.1, r.sub.2, and r.sub.3 are the effective momentarms at which tendons C1, C3, and C5 attach, and T1, T2, T3, T4, T5, andT6 are the tensions in respective tendons C1, C2, C3, C4, C5, and C6.The model that leads to Equation 4A applies to a specific set ofgeometric or mechanical characteristics of the instrument includingjoints 810, 820, and 830 including that: rotation axes z1, z2, and z3are parallel and lie in the same plane; tendons C1 and C2, C3 and C4, orC5 and C6 respectively attach at effective moment arm r1, r2, or r3; andtendons C1, C3, and C5 operate on respective joints 810, 820, and 830 inrotation directions opposite from the operation of tendons C2, C4, andC6, respectively.

[ τ 1 τ 2 τ 3 ] = [ r 1 - r 1 r 2 - r 2 r 3 - r 3 0 0 r 2 - r 2 r 3 - r3 0 0 0 0 r 3 - r 3 ] .Math. [ T .Math. .Math. 1 T .Math. .Math. 2 T.Math. .Math. 3 T .Math. .Math. 4 T .Math. .Math. 5 T .Mat h. .Math. 6 ]Equation .Math. .Math. 4 .Math. A

FIGS. 8B and 8C illustrate characteristics of a medical instrumentincluding joints 810 and 820 with respective rotation axes z1 and z2that are perpendicular to each other. In general, the net torque at eachjoint 810 and 820 depends on the tensions in the tendons passing throughthe joint to the distal end and the effective moment arms associatedwith the tendons relative to the actuation axis of the joint. FIG. 8Cshows a view of a base of joint 810 to illustrate a typical example inwhich each tendon C1, C2, C3, and C4 operates at different moment armsabout axes z1 and z2. Considering joints 810 and 820 as an isolatedsystem or the last two actuated joints on the distal end of aninstrument, the net torques τ.sub.1 and τ.sub.2 on joints 810 and 820are related to the tensions T1, T2, T3, and T4 in respective tendons C1,C2, C3, and C4 as indicated in Equation 4B. In particular, joint 820 issubject to a net torque T2 that depends on tension T3 in tendon C3 and amoment arm α32 relative to axis z2 at which tendon C3 attaches to joint820 and the tension T4 in tendon C4 and a moment arm α42 relative toaxis z2 at which tendon C4 attaches to joint 820. Torque τ.sub.1 onjoint 810 depends on the tensions T1 and T2 in the tendons C1 and C2attached to joint 810, the tensions T3 and T4 in the tendons C3 and C4attached to joint 820, and the moment arms α11, α21, α31, and α41.Moment arms α21 and α41 are assigned with a negative sign becausepulling tendons C2 and C4 creates the rotation in a direction oppositefrom the convention-defined positive direction for torque τ.sub.1 onjoint 810. For the same reason, moment arm α31 is also assigned with anegative sign as pulling tendon C3 causes rotation opposite to thedirection of positive rotation of joint 820.

[ τ 1 τ 2 ] = [ a .Math. .Math. 11 - a .Math. .Math. 21 a .Math. .Math.31 - a .Math. .Math . 41 0 0 - a .Math. .Math. 32 a .Math. .Math. 42 ]□[ T .Math. .Math. 1 T .Math. .Math. 2 T .Mat h. .Math. 3 T .Math..Math. 4 ] Equation .Math. .Math. 4 .Math. B

It should be appreciated that a similar method to compute the matrix Ain Equation 4 can be employed when the j oint axes are neither parallelor perpendicular to each other but rather at an arbitrary relativeorientation, by computing accordingly the moment arms of each tendonwith respect to each joint axis.

FIG. 9A shows a portion 900 of an instrument including a continuousflexible joint 910 such as is commonly found in medical catheters,endoscopes for the gastrointestinal tract, the colon and the bronchia,guide wires, and some other endoscopic instruments such as graspers andneedles used for tissue sampling. Joint 910 is similar to the flexiblestructure described above with reference to FIG. 3B. However, joint 910is manipulated through the use of three or more tendons 920 to provide ajoint with two degrees of freedom of motion. For example, FIG. 9B showsa base view of an embodiment in which four tendons 920, which arelabeled c 1, c 2, c 3, and c 4 in FIG. 9B, connect to an end of flexiblejoint 910. A difference in the tensions in tendons c 1 and c 2 can turnjoint 910 in a first direction, e.g., cause rotation about an X axis,and a difference in the tensions in tendons c 3 and c 4 can turn joint910 in a second direction that is orthogonal to the first direction,e.g., cause rotation about a Y axis. The components τ.sub.X and τ.sub.Yof the net torque tending to bend joint 910 can be determined fromtensions T1, T2, T3, and T4 respectively in tendons c 1, c 2, c 3, and c4 as indicated in Equation 4C. As can be seen from Equation 4C,equations for torque components τ.sub.X and τ.sub.Y are not coupled inthat component τ.sub.X depends only on tensions T1 and T2 and componentτ.sub.Y depends only on tensions T3 and T4.

[ τ X τ Y ] = [rx - rx 0 0 0 0 ry - ry ] .Math. .Math. T .Math. .Math. 1T .Math. .Math. 2 T .Math. .Math. 3 T .Math. .Math. 4 .Math. Equation.Math. .Math. 4 .Math. C

FIG. 9C illustrates a base view of an embodiment that uses three tendons920, which are labeled c 1, c 2, and c 3 in FIG. 9C, to actuate joint910. With this configuration, the components τ.sub.X and τ.sub.Y of thenet torque tending to bend joint 910 can be determined from tensions T1,T2, and T3 respectively in tendons c 1, c 2, and c 3 as indicated inEquation 4D where ra is the moment arm of tendon c 1 about the X axis,-rb is the moment arm of tendons c 2 and c 3 about the X axis, and rcand -rc are the respective moment arms of tendons c 2 and c 3 about theY axis. Moment arms of tendons c 2 and c 3 about X-axis are assignedwith a negative sign by convention because pulling tendons c 2 and c 3will bend joint 910 in a direction opposite from the direction thatpulling tendon c 1 bends joint 910 about the X axis. For the samereason, the moment arm of tendon c 3 about Y-axis is assigned a negativesign by convention.

[ τ X τ Y ] = [ ra - rb - rb 0 rc - rc ] □ [ T .Math. .Math. 1 T .Math..Math. 2 T .Math. .M ath. 3 ] Equation .Math. .Math. 4 .Math. D

FIG. 9D illustrates an embodiment in which a flexible instrument 950,e.g., a flexible catheter, contains two joints. A joint 910 is actuatedthrough tendons 920 to provide two degrees of freedom of motion, and ajoint 940 is actuated through tendons 930 to provide another two degreesof freedom of motion. FIG. 9E illustrates the base of joint 940 in aspecific case that uses three tendons 920 (labeled c 1, c 2, and c 3 inFIG. 9E) for joint 910 and three tendons 930 (labeled c 4, c 5, and c 6in FIG. 9E) for joint 940. The relationships between torques and forcesin the most distal joint 910 may be modeled using Equation 4D above.However, the torques in joint 940 depend on the tensions in all of thetendons 920 and 930 that pass through joint 940. In this example, thejoint 940 is implemented using a flexible section. The torques andtensions in instrument 950 may thus be related in one specific exampleas indicated in Equation 4E. In Equation 4E, τ1.sub.X and τ1.sub.Y aretorque components in joint 910, τ2.sub.X and τ2.sub.Y are torquecomponents in joint 940, ra, rb, and rc are the magnitudes of momentarms, T1, T2, and T3 are tensions in tendons 920, and T4, T5, and T6 aretensions in tendons 930.

[ τ2 X τ2 Y τ1 X τ1 Y] = [ - ra rb rb ra - rb - rb 0 - rc rc 0 rc - rc 00 0 ra - rb - rb 0 0 0 0 rc - rc ] □ [ T .Math. .Math. 1 T .Math. .Math.2 T .Math. .Math. 3 T .Math. .Math. 4 T .Math. . Math. 5 T .Math. .Math.6 ] Equation .Math. .Math. 4 .Math. E

Equations 4A to 4E illustrate that in many medical instruments theproblem of finding tensions that provide a particular torque in the mostdistal joint can be solved independently of the other tensions in thesystem. More generally, the joint torque for each joint depends on thetensions in the tendons that connect to that joint and on the tensionsapplied to more distal joints. Step 735 of processes 700 and 700B ofFIGS. 7A and 7B can thus be performed using a process that iterativelyanalyzes joints in a sequence from the distal end of the instrumenttoward the proximal end of the instrument to determine a set of tensionsthat produces a given set of joint torques.

FIG. 10 illustrates an embodiment in which an instrument 1000 includesthree joints 1010-1, 1010-2, 1010-3, generically referred to as joints1010. Each joint 1010 is actuated through four tendons 1020-1, 1020-2,1020-3, 1020-4, generically referred to as tendons 1020, to provide adegree of freedom of motion. Actuators 1040-1, 1040-2, 1040-3, 1040-4,generically referred to as actuators 1040, are coupled to tendons 1020so that torques τ.sub.A1 and τ.sub.A4 applied to actuators 1040 aretransmitted distally through tendons 1020 to joints 1010. Torquesτ.sub.A1 to τ.sub.A4 generate tensions T.sub.1 to T.sub.4 in tendons1020. Each joint 1010 is coupled to each of tendons 1020 such that aposition of each joint 1010 is adjusted when any one tendon 1020 isactuated by a corresponding actuator 1040. Torques τ.sub.1 to τ.sub.3can correspond to a pitch torque, a yaw torque, and a grip torque. Thepitch torque is depicted in FIG. 10 as generating motion perpendicularto a plane of motion for the yaw torque. Torques τ.sub.1 to τ.sub.3 areapplied to joints 1010 when actuators 1040 apply torques τ.sub.A1 toτ.sub.A4.

The control system 1050 can operate actuators 1040 to generate tensionsin tendons 1020. The control system 1050 can enforce a minimum tensionT.sub.MIN such that tension in each of tendons 1020 exceeds a selectedminimum tension T.sub.MIN. As a result, the relationships betweenactuator positions and degrees of freedom can be derived using Equation2A, with the number of actuators M being equal to 4 and the number ofdegrees of freedom of motion N being equal to 3. In this regard,relationships between actuator positions θ.sub.A1 to θ.sub.A4 anddegrees of freedom θ.sub.1 to θ.sub.3 and θ.sub.T may be modeled usingEquation 2B below (θ=Cθ.sub.A). In this embodiment, θ.sub.1 to θ.sub.3correspond to degrees of freedom of motion, e.g., a pitch degree offreedom, a yaw degree of freedom, and a grip degree of freedom. θ.sub.Tcorresponds to a tension degree of freedom to be used for constrainingtensions in tendons 1020 to be greater than or equal to a minimumtension T.sub.MIN. The coefficients b.sub.IJ for index I=1 to 4 andindex J=1 to 4 are selected such that the column associated with thetension degree of freedom θ.sub.T is linearly independent of the otherdegrees of freedom. The coefficients b.sub.IJ by further represent thecoupling between actuator positions and joint positions.

[ θ 1 θ 2 θ 3 θ T ] = [b 11 b 12 b 13 b 14 b 21 b 22 b 23 b 24 b 31 b 32b 33 b 34 b 41 b 42 b 43 b 44 ] □ [ θ A .Math..Math. 1 θ A .Math. .Math.2 θ A .Math. .Math. 3 θ A .Math. .Math . 4 ] Equation .Math. .Math. 2.Math. B

Equation 5A can be used to derive the relationships between actuatortorques and joint torques. In particular, the relationships betweenactuator torques τ.sub.A1 and τ.sub.A4 and joint torques τ.sub.1 toτ.sub.3 and τ.sub.BIAS may be modeled using Equation 5B below(τ.sub.A=D[τ.sub.1, τ.sub.2, τ.sub.3, 0].sup.T+D[0, 0, 0, τ.sub.BIAS]).Matrix D of Equation 5B can be determined by taking the transpose ofcoupling Matrix C of Equation 2B. Bias parameter τ.sub.BIAS can bedetermined using the processes described with respect to Equation 5A.Equation 5B can be used to determine the actuator torques to apply toactuators 1040.

[ τ A .Math. .Math. 1 τ A .Math. .Math. 2 τ A .Math. .Math. 3 τ A .Math..Math. 4 ] = [ d 1 d 12 d 13 d 14 d 21 d 22 d 23 d 24 d 31 d 32 d 33 d34 d 41 d 42 d 43 d 44 ] .Math. [τ 1 τ 2 τ 3 0 ] + [ d 11 d 12 d 13 d 14d 21 d 22 d 23 d 24 d 31 d 32 d 33 d 34 d 41 d 42 d 43 d 44 ] □ [ 0 0 0τ BIAS ] Equation .Math. .Math. 5 .Math. B

Referring to FIG. 11 , process 1100 is an iterative process used forcomputing tensions that produce a given set of joint torques. Process1100 can use a process similar to that described for Equation 5A tooffset the torques applied by the actuators and thereby offset thetensions applied to the transmission systems. In particular, τ.sub.BIAScan be selected to provide offset tensions that achieve a particularnominal or target tension.

In the example shown in FIG. 11 , process 1100 starts with a tensiondetermination for the last or most distal joint and then sequentiallydetermines tensions for joints in an order toward the first or mostproximal joint. Step 1110 initializes an index j, which identifies ajoint for analysis and is initially set to the number L of joints. Step1120 then acquires the torque τ.sub.j for the jth joint. The jointtorque τ.sub.j may, for example, be determined as in step 730 of process700 or step 732 of 700B as described above and may have a singlenon-zero component for a joint providing a single degree of freedom ofmotion or two non-zero components for a joint providing two degrees offreedom of motion.

Step 1130 then calculates the tensions to be directly applied to the jthjoint through the linkages attached to the jth joint in order to producethe net torque, e.g., computed in step 730 or 732 of FIGS. 7A or 7B. Inthe example of FIG. 11 , computation of step 1130 is under theconstraint that one of the directly applied tensions is a target ornominal tension. The nominal tension may be but is not required to bezero so that tension in the transmission system is released oralternatively the minimum tension T.sub.MIN that ensures that thetendons in the transmission systems do not become slack. The nominaltension may but is not required to correspond to a case in whichactuator force is released, e.g., where actuators 640 of FIG. 6 arefreewheeling, in which case the tension may depend on type oftransmission system employed.

In the specific case in which jth joint in the medical instrumentprovides a single degree of freedom of motion and is directly coupled totwo tendons or transmission systems, the joint torque has a singlecomponent that is related to the tensions by a single equation fromamong Equation 4. Step 1130 for the Lth or most distal joint theninvolves solving a linear equation relating the joint torque to the twotensions coupled to the most distal joint. With a single linear equationinvolving two unknown tensions, applying the constraint that one tensionis the nominal tension guarantees a unique solution for the othertension. In particular, the other tension can be uniquely determinedfrom the torque on the most distal joint and the relevant coefficientsof the coupling matrix A. Alternatively, if the Lth joint provides twodegrees of freedom of motion and is coupled to three tendons ortransmission systems, the joint torque has two components andcorresponds to two equations from among the system of equationsrepresented in Equation 4. The two equations involve three tensions, sothat with the constraint that one of the tensions be equal to thenominal tension, the other two tensions can be uniquely determined fromthe components of the joint torque and the relevant components of thecoupling matrix A. It should be noted that the proposed method isgeneral in the sense that, in a similar fashion, if m tendons, with mgreater than three, are connected to the same joint that provides twodegrees of freedom, then (m-2) tensions can be constrained at the sametime to be equal to the nominal tension, while the remaining twotensions will be uniquely determined from the components of the jointtorque and the relevant components of the coupling matrix A.

Step 1130 is initially executed for the most distal joint (i.e., j=L).Substep 1132 of step 1130 initially selects one of the transmissionsystems attached to the most distal joint, and substep 1134 sets thattension to the minimum permitted tension T.sub.MIN for a trialcalculation in substep 1136. Substep 1136 initially calculates tension(or tensions) for the other transmission systems attached to the joint,and the calculated tensions only depend on the computed joint torque andthe other tensions directly applied to the most distal joint. Substep1138 determines whether all of the calculated tensions are greater thanor equal to the minimum permitted tension T.sub.MIN. If not, step 1140selects another of the transmission systems directly coupled to thejoint to be the transmission system with the nominal tension whensubsteps 1134 and 1136 are repeated. Once step 1140 determines that thecalculated tension or tensions are all greater than or equal to theminimum allowed tension T.sub.MIN, the determination of the tension forthe most distal joint is complete, and step 1150 decrements the jointindex j before process 1100 branches back from step 1160 for repetitionof step 1120.

Step 1130 for the jth joint in the case of a joint connected to twotransmission systems and providing one degree of freedom of motioninvolves evaluation of a single equation from among the system ofequations represented in Equation 5A. As described above, the nature ofthe coupling matrix A is such that the equation for the jth jointinvolves only the tensions directly coupled to the jth joint and thetensions coupled to more distal joints. Accordingly, if the tensions formore distal joints have already been determined, the equation associatedwith the jth joint involves only two unknowns, which are the tensions inthe transmission systems directly connected to the joint. The constraintthat one of the tensions be the nominal tension allows uniquedetermination of the other tension that is larger than or equal to thenominal tension. The case where the jth joint connects to threetransmission systems and provides two degrees of freedom of motioninvolves evaluation of the two equations associated with the twocomponents of the joint torque. If the tensions for more distal jointshave already been determined, the equations associated with the jthjoint involves only three unknowns, which are the tensions in thetendons directly connected to the joint. The constraint that one of thetensions be the nominal tension allows unique determination of the othertwo tensions that are larger than or equal to the nominal tension.

Process 1100 of FIG. 11 can thus use tension determinations in the orderof the joints from the distal end of the instrument to generate acomplete set of distal tensions that is output in step 1170 when step1160 determines that the most proximal joint has been evaluated. Process1100 can be efficiently implemented using a computer or other computingsystem operating for real time determination of tensions that arechanged at a rate that provides motion smooth enough for medicalprocedures, e.g., at rates of up to 250 Hz or more. Further, theconstraint that each joint has at least one directly applied tension ata target or nominal value provides continuity between the tensionsdetermined at successive times.

While substep 1134 is described as setting the tension in a selectedtransmission system to the minimum tension T.sub.MIN and substep 1138 isdescribed as determining whether all of the tensions are above theminimum tension T.sub.MIN, in other implementations, the nominal tensionfor substep 1134 differs from the threshold tension of substep 1138. Thenominal tension can be a target tension for at least one of thetransmission systems, and the threshold tension can be a tension thatthe calculated tensions in the transmission systems do not exceed or donot fall below. In this regard, the threshold tension can be greaterthan or equal to the nominal tension if the threshold tension is amaximum tension T.sub.MAX, or can be less than or equal to the nominaltension if the threshold tension is a minimum tension T.sub.MIN.

While step 1130 is described with respect to achieving tensions above a(non-zero) minimum tension T.sub.MIN, in some implementations, thenominal tension is a maximum allowed tension T.sub.MAX or some othertension in between the minimum tension T.sub.MIN and the maximum tensionT.sub.MAX. Rather than determining whether all of the calculatedtensions are greater than or equal to the minimum permitted tensionT.sub.MIN, substep 1138 determines whether all of the calculatedtensions are less than or equal to the maximum allowed tensionT.sub.MAX. In other implementations, when the nominal tension is betweenthe maximum allowed tension T.sub.MAX and the minimum allowed tensionT.sub.MIN, either all of the calculated tensions are greater than orequal to the nominal tension or all of the calculated tensions are lessthan or equal to the nominal tension.

In some implementations, Process 1100 is executed in conjunction withone or more steps of Process 500. For example, any of the correctionsdescribed herein, such as but not limited to those provided by steps530, 535, 540, 550, 740, and 745, can be applied to Process 1100. Thesecorrections may override the tensions computed as part of step 1130. Inthis regard, the calculated tensions at steps 1130, 1150, 1160 can beoverridden such that the applied distal tensions may differ from thecalculated tensions. For example, if the nominal tension is a minimumtension T.sub.MIN or some other nominal tension below which thecalculated tensions do not fall, the calculated tensions may saturate ata maximum tension T.sub.MAX to prevent the transmission systems frombeing damaged from excessive tensions. If the nominal tension is amaximum tension T.sub.MAX or some other nominal tension above which thecalculated tensions do not exceed, the calculated tensions may saturateat a minimum tension T.sub.MIN to prevent the transmission systems fromgoing slack. The processes described above and elsewhere in thisdisclosure can be implemented or controlled using software that may bestored on computer readable media such as electronic memory or magneticor optical disks for execution by a general purpose computer.Alternatively, control of or calculations employed in theabove-described processes can be implanted using application-specifichardware or electronics.

Although the invention has been described with reference to particularembodiments, the description is only an example of the invention’sapplication and should not be taken as a limitation. For example, typesof instruments that can be controlled vary in implementations. FIG. 12Ais a simplified diagram of another example of a medical instrumentsystem 1200 according to some embodiments. In some embodiments, medicalinstrument system 1200 may be used as medical instrument in animage-guided medical procedure performed with a teleoperated ornon-teleoperated medical system. In some examples, medical instrumentsystem 1200 may be used for non-teleoperational exploratory proceduresor in procedures involving traditional manually operated medicalinstruments, such as endoscopy. Optionally medical instrument system1200 may be used to gather (i.e., measure) a set of data pointscorresponding to locations within anatomic passageways of a patient,such as patient P.

Medical instrument system 1200 includes elongate device 1202 coupled toa drive unit 1204. Elongate device 1202 includes a flexible body 1216having proximal end 1217 and distal end 1218 (also called “tip portion1218” when the distal end includes a portion of a tip). In someembodiments, flexible body 1216 has an approximately 3 mm outerdiameter. Other flexible body outer diameters may be larger or smaller.

Medical instrument system 1200 further includes a tracking system 1230for determining the position, orientation, speed, velocity, pose, and/orshape of flexible body 1216 at distal end 1218 and/or of one or moresegments 1224 along flexible body 1216 using one or more sensors and/orimaging devices as described in further detail below. The entire lengthof flexible body 1216, between distal end 1218 and proximal end 1217,may be effectively divided into segments 1224. Tracking system 1230 mayoptionally be implemented as hardware, firmware, software or acombination thereof which interact with or are otherwise executed by oneor more computer processors, which may include the processors of controlsystem 150 in FIG. 1 .

Tracking system 1230 may optionally track distal end 1218 and/or one ormore of the segments 1224 using a shape sensor 1222. Shape sensor 1222may optionally include an optical fiber aligned with flexible body 1216(e.g., provided within an interior channel (not shown) or mountedexternally). In one embodiment, the optical fiber has a diameter ofapproximately 1200 µm. In other embodiments, the dimensions may belarger or smaller. The optical fiber of shape sensor 1222 forms a fiberoptic bend sensor for determining the shape of flexible body 1216. Inone alternative, optical fibers including Fiber Bragg Gratings (FBGs)are used to provide strain measurements in structures in one or moredimensions. Various systems and methods for monitoring the shape andrelative position of an optical fiber in three dimensions are describedin U.S. Pat. Application Ser. No. 11/180,389 (filed Jul. 13, 2005)(disclosing “Fiber optic position and shape sensing device and methodrelating thereto”); U.S. Pat. Application Ser. No. 12/047,056 (filed onJul. 16, 2004) (disclosing “Fiber-optic shape and relative positionsensing”); and U.S. Pat. No. 6,389,187 (filed on Jun. 17, 1998)(disclosing “Optical Fibre Bend Sensor”), which are all incorporated byreference herein in their entireties. Sensors in some embodiments mayemploy other suitable strain sensing techniques, such as Rayleighscattering, Raman scattering, Brillouin scattering, and Fluorescencescattering. In some embodiments, the shape of flexible body 1216 may bedetermined using other techniques. For example, a history of the distalend pose of flexible body 1216 can be used to reconstruct the shape offlexible body 1216 over the interval of time. In some embodiments,tracking system 1230 may optionally and/or additionally track distal end1218 using a position sensor system 1220. Position sensor system 1220may be a component of an EM sensor system with position sensor system1220 including one or more conductive coils that may be subjected to anexternally generated electromagnetic field. Each coil of EM sensorsystem including the position sensor system 1220 then produces aninduced electrical signal having characteristics that depend on theposition and orientation of the coil relative to the externallygenerated electromagnetic field. In some embodiments, position sensorsystem 1220 may be configured and positioned to measure six degrees offreedom, e.g., three position coordinates X, Y, Z and three orientationangles indicating pitch, yaw, and roll of a base point or five degreesof freedom, e.g., three position coordinates X, Y, Z and two orientationangles indicating pitch and yaw of a base point. Further description ofa position sensor system is provided in U.S. Pat. No. 6,380,732 (filedAug. 11, 1999) (disclosing “Six-Degree of Freedom Tracking System Havinga Passive Transponder on the Object Being Tracked”), which isincorporated by reference herein in its entirety.

In some embodiments, tracking system 1230 may alternately and/oradditionally rely on historical pose, position, or orientation datastored for a known point of an instrument system along a cycle ofalternating motion, such as breathing. This stored data may be used todevelop shape information about flexible body 1216. In some examples, aseries of positional sensors (not shown), such as electromagnetic (EM)sensors similar to the sensors in position sensor system 1220 may bepositioned along flexible body 1216 and then used for shape sensing. Insome examples, a history of data from one or more of these sensors takenduring a procedure may be used to represent the shape of elongate device1202, particularly if an anatomic passageway is generally static.

Flexible body 1216 includes a channel 1221 sized and shaped to receive amedical instrument 1226. FIG. 12B is a simplified diagram of flexiblebody 1216 with medical instrument 1226 extended according to someembodiments. In some embodiments, medical instrument 1226 may be usedfor procedures such as surgery, biopsy, ablation, illumination,irrigation, or suction. Medical instrument 1226 can be deployed throughchannel 1221 of flexible body 1216 and used at a target location withinthe anatomy. Medical instrument 1226 may include, for example, imagecapture probes, biopsy instruments, laser ablation fibers, and/or othersurgical, diagnostic, or therapeutic tools. Medical tools may includeend effectors having a single working member such as a scalpel, a bluntblade, an optical fiber, an electrode, and/or the like. Other endeffectors may include, for example, forceps, graspers, scissors, clipappliers, and/or the like. Other end effectors may further includeelectrically activated end effectors such as electrosurgical electrodes,transducers, sensors, and/or the like. In various embodiments, medicalinstrument 1226 is a biopsy instrument, which may be used to removesample tissue or a sampling of cells from a target anatomic location.Medical instrument 1226 may be used with an image capture probe alsowithin flexible body 1216. In various embodiments, medical instrument1226 may be an image capture probe that includes a distal portion with astereoscopic or monoscopic camera at or near distal end 1218 of flexiblebody 1216 for capturing images (including video images) that areprocessed by a visualization system 1231 for display and/or provided totracking system 1230 to support tracking of distal end 1218 and/or oneor more of the segments 1224. The image capture probe may include acable coupled to the camera for transmitting the captured image data. Insome examples, the image capture instrument may be a fiber-optic bundle,such as a fiberscope, that couples to visualization system 1231. Theimage capture instrument may be single or multi-spectral, for examplecapturing image data in one or more of the visible, infrared, and/orultraviolet spectrums. Alternatively, medical instrument 1226 may itselfbe the image capture probe. Medical instrument 1226 may be advanced fromthe opening of channel 1221 to perform the procedure and then retractedback into the channel when the procedure is complete. Medical instrument1226 may be removed from proximal end 1217 of flexible body 1216 or fromanother optional instrument port (not shown) along flexible body 1216.

Medical instrument 1226 may additionally house cables, linkages, orother actuation controls (not shown) that extend between its proximaland distal ends to controllably bend distal end of medical instrument1226. Steerable instruments are described in detail in U.S. Pat. No.7,316,681 (filed on Oct. 4, 2005) (disclosing “Articulated SurgicalInstrument for Performing Minimally Invasive Surgery with EnhancedDexterity and Sensitivity”) and U.S. Pat. Application Ser. No.12/286,644 (filed Sept. 30, 2008) (disclosing “Passive Preload andCapstan Drive for Surgical Instruments”), which are incorporated byreference herein in their entireties.

Flexible body 1216 may also house cables, linkages, or other steeringcontrols (not shown) that extend between drive unit 1204 and distal end1218 to controllably bend distal end 1218 as shown, for example, bybroken dashed line depictions 1219 of distal end 1218. In some examples,at least four cables are used to provide independent “up-down” steeringto control a pitch of distal end 1218 and “left-right” steering tocontrol a yaw of distal end 1281. Steerable catheters are described indetail in U.S. Pat. aaplication Ser. No. 13/274,208 (filed Oct. 14,2011) (disclosing “Catheter with Removable Vision Probe”), which isincorporated by reference herein in its entirety. In embodiments inwhich medical instrument system 1200 is actuated by a teleoperationalassembly, drive unit 1204 may include drive inputs that removably coupleto and receive power from drive elements, such as actuators, of theteleoperational assembly. In some embodiments, medical instrument system1200 may include gripping features, manual actuators, or othercomponents for manually controlling the motion of medical instrumentsystem 1200. Elongate device 1202 may be steerable or, alternatively,the system may be non-steerable with no integrated mechanism foroperator control of the bending of distal end 1218. In some examples,one or more lumens, through which medical instruments can be deployedand used at a target surgical location, are defined in the walls offlexible body 1216.

In some embodiments, medical instrument system 1200 may include aflexible bronchial instrument, such as a bronchoscope or bronchialcatheter, for use in examination, diagnosis, biopsy, or treatment of alung. Medical instrument system 1200 is also suited for navigation andtreatment of other tissues, via natural or surgically created connectedpassageways, in any of a variety of anatomic systems, including thecolon, the intestines, the kidneys and kidney calices, the brain, theheart, the circulatory system including vasculature, and/or the like.

The information from tracking system 1230 may be sent to a navigationsystem 1232 where it is combined with information from visualizationsystem 1231 and/or the preoperatively obtained models to provide thephysician, clinician, or surgeon or other operator with real-timeposition information. In some examples, the real-time positioninformation may be displayed on a display system 1210 for use in thecontrol of medical instrument system 1200. In some examples, a controlsystem may utilize the position information as feedback for positioningmedical instrument system 1200. Various systems for using fiber opticsensors to register and display a surgical instrument with surgicalimages are provided in U.S. Pat. Application Ser. No. 13/107,562, filedMay 13, 2011, disclosing, “Medical System Providing Dynamic Registrationof a Model of an Anatomic Structure for Image-Guided Surgery,” which isincorporated by reference herein in its entirety.

In some examples, medical instrument system 1200 may be teleoperated. Insome embodiments, teleoperational manipulator assembly 1233 may bereplaced by direct operator control. In some examples, the directoperator control may include various handles and operator interfaces forhand-held operation of the instrument.

Various adaptations and combinations of features of the embodimentsdisclosed are within the scope of the invention as defined by thefollowing claims.

1-39. (canceled)
 40. An instrument system comprising: a plurality ofactuators; an instrument comprising: an end portion, and a plurality oftransmission systems, each transmission system coupling the end portionto an actuator of the plurality of actuators such that the plurality ofactuators is operable to drive the plurality of transmission systems tomove the end portion; and a control system operably connected to theplurality of actuators, the control system configured to executeoperations comprising: determining a difference between a currentconfiguration of the end portion and a desired configuration of the endportion, and determining a plurality of tensions to apply to theplurality of transmission systems based on the difference, wherein atension of the plurality of tensions is maintained at a maximum tensionand a remainder of the plurality of tensions is no more than the maximumtension.
 41. The instrument system of claim 40, wherein all tensions ofthe plurality of tensions are each no less than a non-zero minimumtension.
 42. The instrument system of claim 41, wherein: the operationsfurther comprise: operating the plurality of actuators to apply theplurality of tensions to the plurality of transmission systems such thatall tensions of the plurality of tensions are each no less than themaximum tension and no more than the non-zero minimum tension.
 43. Theinstrument system of claim 42, wherein: operating the plurality ofactuators to apply the plurality of tensions to the plurality oftransmission systems comprises: selecting, based on the non-zero minimumtension, a transmission system of the plurality of transmission systems,and operating the plurality of actuators to apply the tension of theplurality of tensions to the transmission system of the plurality oftransmission systems.
 44. The instrument system of claim 40, wherein theoperations further comprise: determining a current velocity of anactuator of the plurality of actuators; determining a damping parameterbased on the current velocity and based on a desired velocity of theactuator of the plurality of actuators; and operating the plurality ofactuators to apply the plurality of tensions to the plurality oftransmission systems based on the damping parameter.
 45. The instrumentsystem of claim 44, wherein: determining the damping parameter andoperating the plurality of actuators occur in response to the currentvelocity being no less than a threshold velocity.
 46. The instrumentsystem of claim 40, wherein: determining the plurality of tensions toapply to the plurality of transmission systems based on the differenceis further based on maintaining the tension of the plurality of tensionsat the maximum tension and the remainder of the plurality of tensions atno more than the maximum tension.
 47. The instrument system of claim 46,wherein: the plurality of tensions are a plurality of first tensions;and the operations further comprise: determining a plurality of secondtensions based on the difference; and in response to at least onetension of the plurality of second tensions being no less than athreshold tension: determining the plurality of first tensions to applyto the plurality of transmission systems, and operating the plurality ofactuators to apply the plurality of first tensions to the plurality oftransmission systems.
 48. The instrument system of claim 47, wherein:the operations further comprise: in response to at least one tension ofthe plurality of second tensions being less than the threshold tension:determining a plurality of third tensions to apply to the plurality oftransmission systems based on the difference and based on maintainingthe plurality of third tensions at no less than a minimum tension, andoperating the plurality of actuators to apply the plurality of thirdtensions to the plurality of transmission systems.
 49. The instrumentsystem of claim 47, wherein: the operations further comprise: inresponse to at least one tension of the plurality of second tensionsbeing less than the threshold tension: determining a plurality of thirdtensions to apply to the plurality of transmission systems based on thedifference and based on one or more constant offset tensions, andoperating the plurality of actuators to apply the plurality of thirdtensions to the plurality of transmission systems.
 50. One or morenon-transitory computer readable media storing instructions that areexecutable by a processing device, and upon such execution cause theprocessing device to perform operations comprising: determining adifference between a current configuration of an end portion of aninstrument and a desired configuration of the end portion of theinstrument; determining a plurality of tensions to apply to a pluralityof transmission systems of the instrument based on the difference,wherein the plurality of transmission systems is coupled to move the endportion; and operating a plurality of actuators to apply the pluralityof tensions to the plurality of transmission systems, wherein a tensionof the plurality of tensions is maintained at a maximum tension and aremainder of the plurality of tensions at no more than the maximumtension.
 51. The one or more non-transitory computer readable media ofclaim 50, wherein: all tensions of the plurality of tensions are each noless than a non-zero minimum tension; and operating the plurality ofactuators to apply the plurality of tensions to the plurality oftransmission systems comprises: operating the plurality of actuators toapply the plurality of tensions to the plurality of transmission systemssuch that all tensions of the plurality of tensions are each no lessthan the maximum tension and no more than the non-zero minimum tension.52. The one or more non-transitory computer readable media of claim 50,wherein the operations further comprise: determining a current velocityof an actuator of the plurality of actuators; determining a dampingparameter based on the current velocity and based on a desired velocityof the actuator of the plurality of actuators; and operating theplurality of actuators to apply the plurality of tensions to theplurality of transmission systems based on the damping parameter. 53.The one or more non-transitory computer readable media of claim 50,wherein: the plurality of tensions are a plurality of first tensions;determining the plurality of first tensions to apply to the plurality oftransmission systems based on the difference is further based onmaintaining the tension of the plurality of first tensions at themaximum tension and the remainder of the plurality of first tensions atno more than the maximum tension; and the operations further comprise:determining a plurality of second tensions based on the difference; inresponse to at least one tension of the plurality of second tensionsbeing no less than a threshold tension: determining the plurality offirst tensions to apply to the plurality of transmission systems, andoperating the plurality of actuators to apply the plurality of firsttensions to the plurality of transmission systems; and in response to atleast one tension of the plurality of second tensions being less thanthe threshold tension: determining a plurality of third tensions toapply to the plurality of transmission systems based on the differenceand based on maintaining the plurality of third tensions at no less thana minimum tension, and operating the plurality of actuators to apply theplurality of third tensions to the plurality of transmission systems.54. The one or more non-transitory computer readable media of claim 50,wherein: the plurality of tensions is a plurality of first tensions;determining the plurality of first tensions to apply to the plurality oftransmission systems based on the difference is further based onmaintaining the tension of the plurality of first tensions at themaximum tension and the remainder of the plurality of first tensions atno more than the maximum tension; and the operations further comprise:determining a plurality of second tensions based on the difference; inresponse to at least one tension of the plurality of second tensionsbeing no less than a threshold tension: determining the plurality offirst tensions to apply to the plurality of transmission systems,operating the plurality of actuators to apply the plurality of firsttensions to the plurality of transmission systems, and in response to atleast one tension of the plurality of second tensions being less thanthe threshold tension: determining a plurality of third tensions toapply to the plurality of transmission systems based on the differenceand based on one or more constant offset tensions, and operating theplurality of actuators to apply the plurality of third tensions to theplurality of transmission systems.
 55. A method of operating aninstrument, the method comprising: determining a difference between acurrent configuration of an end portion of the instrument and a desiredconfiguration of the end portion of the instrument; determining aplurality of tensions to apply to a plurality of transmission systems ofthe instrument based on the difference, wherein the plurality oftransmission systems is coupled to move the end portion; and operating aplurality of actuators to apply the plurality of tensions to theplurality of transmission systems, wherein a tension of the plurality oftensions is maintained at a maximum tension and a remainder of theplurality of tensions at no more than the maximum tension.
 56. Themethod of claim 55, wherein: all tensions of the plurality of tensionsare each no less than a non-zero minimum tension; and operating theplurality of actuators to apply the plurality of tensions to theplurality of transmission systems comprises: operating the plurality ofactuators to apply the plurality of tensions to the plurality oftransmission systems such that all tensions of the plurality of tensionsis no less than the maximum tension and no more than the non-zerominimum tension.
 57. The method of claim 55, further comprising:determining a current velocity of an actuator of the plurality ofactuators, determining a damping parameter based on the current velocityand based on a desired velocity of the actuator of the plurality ofactuators, and operating the plurality of actuators to apply theplurality of tensions to the plurality of transmission systems based onthe damping parameter.
 58. The method of claim 55, wherein: theplurality of tensions are a plurality of first tensions; determining theplurality of first tensions to apply to the plurality of transmissionsystems based on the difference is further based on maintaining thetension of the plurality of first tensions at the maximum tension andthe remainder of the plurality of first tensions at no more than themaximum tension; and the method further comprises: determining aplurality of second tensions based on the difference; in response to atleast one tension of the plurality of second tensions being no less thana threshold tension: determining the plurality of first tensions toapply to the plurality of transmission systems, and operating theplurality of actuators to apply the plurality of first tensions to theplurality of transmission systems; and in response to at least onetension of the plurality of second tensions being less than thethreshold tension: determining a plurality of third tensions to apply tothe plurality of transmission systems based on the difference and basedon maintaining the plurality of third tensions at no less than a minimumtension; and operating the plurality of actuators to apply the pluralityof third tensions to the plurality of transmission systems.
 59. Themethod of claim 55, wherein: the plurality of tensions are a pluralityof first tensions; determining the plurality of first tensions to applyto the plurality of transmission systems based on the difference isfurther based on maintaining the tension of the plurality of firsttensions at the maximum tension and the remainder of the plurality offirst tensions at no more than the maximum tension; and the methodfurther comprises: determining a plurality of second tensions based onthe difference; in response to at least one tension of the plurality ofsecond tensions being no less than a threshold tension: determining theplurality of first tensions to apply to the plurality of transmissionsystems, and operating the plurality of actuators to apply the pluralityof first tensions to the plurality of transmission systems; and inresponse to at least one tension of the plurality of second tensionsbeing less than the threshold tension: determining a plurality of thirdtensions to apply to the plurality of transmission systems based on thedifference and based on one or more constant offset tensions, andoperating the plurality of actuators to apply the plurality of thirdtensions to the plurality of transmission systems.